One day after school in January this year, Isabelle walked to the high street in East Grinstead, West Sussex, where her mother works in a shop selling gifts and clothes. She was with her boyfriend, Alex, who would be meeting her mum for the first time. “It kind of took her by surprise a bit,” Isabelle says, remembering the awkwardness of the moment.

When that was over, Isabelle sprang another surprise: a few hours earlier she had received an offer to read Earth sciences at Oxford University. “Mum gave me a big hug,” says Isabelle, who is now 18. “She was absolutely over the moon for me.”

That evening, Isabelle made herself pasta for dinner and sat down to think about it. Over the past month she had convinced herself that she wouldn’t get into Oxford, and that she didn’t belong there anyway. She remembered the terrible night after her first interview, sitting in a college room in tears, feeling like an impostor.

But now, with an offer letter sitting on the table, she started to have a change of heart. She was going to be the first person in her extended family to go to university, and this was an offer from one of the best universities in the world. “I thought, I’ve got to do it,” she says. Late that night she sent me an email about how she was feeling. “It hasn’t really sunk in yet, to be honest,” she wrote. “But I’m pleased.”

Isabelle and I first met in March last year at Sackville school, the West Sussex comprehensive she attended from the age of 11. The school is close to where I grew up, and for the past year and a half I have been mentoring students there, trying to help them get into Oxford, Cambridge, University College London and other leading universities. It started as a casual offer of help to my local school and went on to become an all-consuming project – the thing my friends would ask about first when I saw them, and a challenge that has given me more satisfaction than any story I’ve written as a journalist.

High-achieving students at state schools like Sackville often lose out in the battle for places at the most selective universities. The application process is supposed to uncover talent and potential, but often seems designed to reward traits such as confidence and polish, handing a significant advantage to applicants whose parents went to university, and whose school knows the subtleties of a good application, often due to decades or even centuries of experience. In the case of many private schools, knowing how to convert great A-levels into places at elite universities is the reason they can charge such high fees.

When I first met Isabelle and her schoolmates, I had just moved home to live with my mother, after my father died suddenly in late 2018. Dad had lived in this area all his life, and when I was growing up he volunteered to help dig various local institutions out of financial difficulty, including a school and a community farm. Helping out at Sackville provided a distraction from my grief, and felt like the kind of civic-minded thing he would do. Added to that, three generations of my relatives have gone to Sackville, since my grandparents settled in this corner of West Sussex as Jewish Czech refugees in the 1940s. These included two aunts, a bunch of cousins and, currently, my cousin’s 12-year-old daughter.

If you are passing through East Grinstead on your way to Lewes or Brighton, you might spot Sackville, crouching behind some high hedges just before the town gives way to fields and villages. It is probably what many people picture when they think of a comprehensive: cheerless 1960s buildings, well over a thousand students, and some very average A-level results, literally: the school’s average A-level grade is a C, which is the national average. It performs above average at GCSE and is rated “Good” by Ofsted; but its sixth form isn’t selective, and around four out of every five students have parents who didn’t go to university.

In recent years, Sackville’s deputy headteacher, Adrian De Souza, had become frustrated that too few of his best sixth-formers were getting places at leading universities. “We talked about it a lot,” he says. “We had the feeling there was something we weren’t doing.” No Sackville student had gone to Oxford or Cambridge since 2013, despite plenty of them having good enough grades – including some who got interviews but didn’t get places. The proportion of school leavers going to the most sought-after Russell Group universities was also disappointing.

De Souza is a preternaturally warm and engaging teacher, who seems to have a running in-joke with every second student we pass in Sackville’s corridors. He felt that, as the resources at his disposal have been squeezed (spending per pupil in England has fallen 8% in real terms since 2009-10), it was becoming harder to compete with the private sector. The six-year Oxbridge dry spell was only a part of the problem, but it was symbolic. De Souza went to Bristol University, and knows that this country’s obsession with Oxbridge borders on the perverse. But he also thinks that what’s possible for students at the local private schools should be possible for his students, too. (Disclaimer: I went to one of these private schools, and to Cambridge University.)

At one point in my first meeting at the school, Isabelle was waved in – a confident girl wearing black jeans and white Converse trainers, with wavy blond hair that she dyes a reasonably convincing ginger. After being introduced, she asked me what she could do to prepare for an application to Oxford and other prestigious universities like Imperial, Manchester and UCL. I didn’t have a good answer ready, but later that night I emailed friends who had also studied at Cambridge. I asked them all: what would you tell her?

“Interview training is imperative,” replied a friend who now works in the City of London. “If you have never been in a situation where someone is challenging your intellect/interest/whole identity, such a massive part of it is just retaining your cool.” Others offered tips about preparatory reading, or emphasised the importance of making sure the students have the confidence to apply in the first place.

A few weeks later, Sackville’s head of sixth form, Helen Valentine, assembled 10 of her highest-achieving year 12s, including Isabelle. They sat in front of me around a U shape of desks in a computer room, wearing casual clothes and chatting among themselves.

For those who wanted to apply for Oxford or Cambridge, or to study medicine, the deadline was about six months away. These students became known among teachers as the “Oxbridge group”, but everything we were doing was supposed to work for Bristol, Durham and all the other Russell Group universities they were applying to at the same time. I told them I would try to give them something approximating the support students from private schools get. We would meet every week or two to talk about their subjects. They seemed receptive, but didn’t ask any questions. I tried to project confidence about the whole thing, because I knew how important a commodity confidence was going to be. But naturally, I also had some doubts.

***

If you want a place at one of Britain’s top universities, you need to beat a lot of very well-prepared, expensively educated young people to get it. A recent report showed that almost half the schools that teach the most privileged 20% of students in the country – mostly private schools and grammars – have at least one dedicated “university adviser”. St Paul’s in London has 12 teachers who are trained as “UK university advisers” and nine staff who act as “counsellors and support staff for US university applications”, according to the school’s website.

And if wealthy parents aren’t content with what their school is giving them, they often top it up with private tutors. “Parents normally say, ‘I need someone who has graduated from that course in the past few years,’” the head of a leading tutoring agency in London tells me. “If you are applying for PPE at Oxford, we will find tutors who have done that course.”

A new book, Social Mobility And Its Enemies, calls this “education’s dark side” and argues that parents are engaging in an “ever-escalating educational arms race”. Lee Elliot Major, the book’s co-author and a professor of social mobility at Exeter University, tells me that in an increasingly complex admissions process, there are big advantages for applicants who know “the rules of the game” – including the subtle art of tailoring your personal statement.

It goes without saying that most state schools don’t have the time or resources to offer this kind of preparation. A school like Sackville gets £4,000 a year to educate each member of its sixth form, a small fraction of most private school fees. Teachers spend most of their time teaching or preparing for class.

“Teachers could go and learn the rules of the game at various careers conferences,” says Nick Hillman, director of the Higher Education Policy Institute, “but do they have time? The conferences I speak at are full of private-school teachers, often ones who are dedicated to uni preparation.” The result is that entry to the most sought-after universities is utterly dominated by private schools, and a narrow group of state schools that are either highly selective, or have a long tradition of getting students into elite universities, or both.

Admissions data obtained by the Guardian from Oxford and Cambridge under freedom of information laws illustrates this clearly. Both universities made about half of their undergraduate offers to state school students in the past few years, with the remainder split roughly evenly between private school and overseas applicants. But the vast majority of the state school offers – more than two-thirds – went to just 300 schools. These schools represent the highest-performing 10% of state schools in the country and are mostly grammar schools, highly selective sixth-form colleges or academies in wealthy areas. They average around five Cambridge offers a year, and four from Oxford, so have plenty of experience in getting the best students in.

Students from the remaining 90% of state schools – roughly 2,700 – get significantly fewer Oxbridge offers. On average, students from these schools, which include most regular comprehensives like Sackville, get an offer from Cambridge once every four years, and an offer from Oxford every five years. And before anyone dismisses this disparity on the grounds that these schools aren’t applying: the figures show that at least one student at most of this country’s schools and colleges applies to Oxford or Cambridge every year.

When top universities boast about their state school intakes, it’s easy to forget this silent majority of frozen-out schools, where the students who get in are statistical outliers. Or, as one of my friends put it when I worked out the figures: “That’s a pretty sad state of affairs for anything resembling a meritocracy.” And when it comes to university applications, failure begets failure, according to Sir Peter Lampl, founder of social mobility charity the Sutton Trust. “It’s hard for state schools to gear up, because they only get one student in every five years,” he says.

That isn’t a bad description of what had been happening at Sackville. The daunting challenge was to help the school jump from the forgotten 90% into the tiny elite.

***

When she was in year 8, Isabelle remembers telling three friends that she wanted to study science at Oxford. She was half joking, half dreaming, she says. “It didn’t seem real, to be honest. It was very much something that people like me didn’t do.”

Five years later, Isabelle and those three friends were all in our little group, including Lucy, applying to study English at Cambridge. Also in the group was Eren, a tall, unflappable young man who spends his weekends either working at a garden centre or climbing sheer rock faces. He grew up in Croydon, south London, before his parents moved to Sussex (his father works in construction and his mother is a yoga teacher). He has a similar memory to Isabelle: aged 13, he told a girl sitting next to him in science class, “I want to do physics at Cambridge”, but remembers thinking, “That’s not really going to happen, is it?”

There were definitely times in my months working with the students when it felt as if it wasn’t going to happen. My notes for the early meetings sometimes just say: “Didn’t email” or “Didn’t come”. I was spending a lot of my time just persuading a few of the students that they were good enough. Eren says the school’s track record played on his mind. “For however many years, no one got in [to Oxbridge], so you think there must be a pretty good reason for that.”

After a month or two, though, I started to have a good feeling about the students. They had the kind of work ethic and grades that top universities expect, and they seemed to enjoy the challenge we had been set. I told them to treat getting into university like a mini extra A-level: something that requires a bit of work every week, reading interesting articles about their chosen subjects, and learning how to talk about what they had read when we met.

Ayo, Sackville’s head boy and one of its best footballers, whose parents had come to England from Nigeria when he was small, prepared for his application to Stanford in California by reading longform articles about economics. Lucy read lesser-known short stories by F Scott Fitzgerald and made interesting connections between them. Eren had been reading fairly advanced books about physics since he was a teenager, and just needed reminding that mentioning them in his application was a good idea. Sometimes our sessions were about sharpening the students’ thoughts, or picking them up if someone or something had knocked their confidence.

As last spring turned into summer, my Tuesday morning volunteering gig was occupying more of my thoughts. I would email ideas to De Souza and Valentine at 1am, while watching Netflix. I used my group chat of university friends to answer questions about courses, colleges and future careers. Two of them took a day off work to do practice interviews, meeting the students one by one. At the end of each interview, I could hear them give the same pep talk: we think you’re good enough for this, so believe in yourself.

When I visited the school, De Souza, Valentine and I would sit in Valentine’s office next to the sixth-form study room at lunchtime, drinking coffee and making plans. It had become a team effort that energised a handful of staff, and it was exciting. We felt these kids were going to do well, and they deserved to. The teachers had worked with most of the students for half a decade, and they deserved it, too.

On a beautiful, sunny day in June, my former tutor at Cambridge agreed to show the students around the university. He gave them tips for their applications, and subjected me to a rapid-fire mock interview in his office to show the students what their own interviews might be like.

On the bus back, the pupils chatted about Love Island, debating who was more of a snake, Maura or Mollie-Mae. I wasn’t sure how they would respond to the visit, but looking back, Valentine says it was a turning point. “They felt they had a really good chance,” she says. “There were no more tears and drama after that. We felt that something was in our grasp, that something special could happen this year.” Eren says it was the visit that convinced him to apply: it had made an unrealistic prospect seem real.

***

Around the time that the Sackville students were putting the final touches to their applications, Dr Marchella Ward, the outreach fellow at Worcester College, Oxford, was challenging her colleagues with a radical proposal. Ward, whose job it is to attract a wider cohort of students to the college, wanted to make this year’s intake – the ones starting their courses this month – “genuinely representative”. She resolved that the students who got offers from Worcester should look like the students nationwide who achieve AAA and above at A-level, in terms of their schools and economic backgrounds.

That meant persuading the college’s admissions tutors to focus on how they were assessing potential in students; to figure out why they were admitting a lot of privileged candidates. One of the key areas they looked at was personal statements – the one-page sales pitch that every applicant has to submit via the Ucas system. As all 21 university advisers at St Paul’s know, there is a particular skill to writing a personal statement for an elite university. It involves a certain type of showing off: talking about a 1971 lecture you came across by a Nobel prize-winning chemist; or linking something you studied at A-level to a review you read in the Times Literary Supplement (which you most definitely did not come across at school). Making those kinds of references suggests to admissions tutors that you are a highly engaged, impressively self-directed learner who will thrive at universities where embracing the specific and the obscure is a way of life.

It’s the oldest trick in the book, and Ward wanted her college to stop falling for it. She felt strongly that the college was missing out on outstanding students in favour of ones who were better coached. “It was about asking tutors to think really hard about what it was that was making them impressed,” she says. “We’ve got to be thinking carefully about why we think potential looks that way.”

When it came to targets, Ward wanted Worcester to move away from thinking about simple binary metrics like state or private school, which she says can always be gamed. Instead she asked her colleagues to pay particular attention to a new dashboard of “contextual” data, provided by the university to its colleges about all Oxford applicants, which ranked every student by factors like what percentage of their school is on free school meals. “It’s about assessing potential in a way that takes all sorts of advantage into account,” she tells me.

By mid-January this year, we knew our efforts at Sackville had paid off. Every student in our group had offers from universities such as Durham, Imperial, LSE, Edinburgh, Manchester and UCL. And then, while I was driving along the motorway on a grey and drizzly morning, I saw an email from Valentine: Isabelle had an offer to read Earth sciences at Oxford – with grades of A*AA. And Grace, another of our applicants, had been accepted by Oxford to study geography, having taken her A-levels last year.

I pulled into the next service station, sat down in a Starbucks to read it again, and messaged my friends Shyam and Frankie, who since doing the practice interviews had become almost as invested as me. I punched the air several times, and worried that the man at the next table would see I had tears in my eyes.

Valentine was on a school trip in Hamburg with Sackville’s headteacher, Julian Grant. “I can only describe it as like an election night, when you’re sitting up waiting for the seats to come in,” she remembers. “I realised it meant an awful lot to very many of us.” She kept refreshing her phone, watching Ucas Track, the website where university offers show up, until the news came through that both Lucy and Eren had offers from Cambridge. “We really felt very proud for the school,” Valentine says. “There was a feeling of elation, first and foremost, for the students, and for you, and for ourselves as well.”

Eren got his offer to study natural sciences at Cambridge via email on his phone first thing in the morning, feeling “as psyched as you can be when you’ve just woken up”. He put a screenshot on his family WhatsApp group. “I think my mum replied first – she was quite chuffed. I think she just said, ‘Well done’, and probably made a joke about posh people.” His dad called him from his office. “He was crying a bit. He said he had told all his friends from work.”

Ayo was offered a place at Stanford, majoring in economics. The final list of offers felt almost unreal; overall, twice as many Sackville students as the year before had offers from Russell Group universities.

What does it prove? “I think the interesting thing about your story is that it puts a big question mark over the admission practices of these universities,” says Nick Hillman, who was an adviser to the former universities minister David Willetts. “The kids who got in, Oxbridge obviously thinks are good enough. And previously Oxbridge would never have found out about them.”

Duncan Exley, former director of the Equality Trust, says he isn’t surprised, either. He points out that social mobility charities like the Brilliant Club, Into University and the Sutton Trust have shown “measurable results” from mentoring talented state school students. But that support is unevenly spread. One of the people interviewed in Exley’s new book, The End of Aspiration? Social Mobility And Our Children’s Fading Prospects, told him: “If you are a kid in Tower Hamlets, you are practically chased down the street by social mobility charities. But in rural Norfolk, there is nobody.”

Marchella Ward’s efforts at Worcester also bore fruit. She says 83% of the college’s offers went to state school students and 20% went to students from areas with low progress rates into higher education, both comfortably above the percentages from those groups who get AAA or above. Several Oxford colleges have asked her to explain how she did it. After thousands of A-level students were downgraded in this year’s exam fiasco, Worcester was the first Oxbridge college to say it would honour its existing offers.

Between Sackville and Worcester, you have two different approaches to solving the problem of access to our most selective universities. You either teach a lot more students the rules of the game – or you change those rules. Some people, like Elliot Major, support sending trained advisers into every school, paid for by the government. Ward says that’s fine as a stopgap until universities get better at assessing potential rather than coaching and polish. “Let’s do that as long as we have to. But as universities, let’s make that time as short as possible,” she says.

The independent Office for Students, which regulates universities, has been running a consultation on changes to the application process; proposals include scrapping personal statements, and the system of applying for university before you get your results. But this has been paused during the pandemic.

All of the Sackville group ended up with the grades they needed, despite the flawed A-level algorithm. Isabelle is in various WhatsApp groups with other students who held offers from Oxford, which lit up with emotional messages when people lost their places on results day. “Some people missed their grades by one, and others were getting Cs and Ds,” she says. Some got their places back, after the government U-turn, or on appeal. Those who didn’t left the group chats.

Of course, none of us had any idea how strange and disrupted their university experience would turn out be. Ayo is beginning his Stanford degree remotely, and Eren says he has “accepted it’s going be different”. One of the students I spoke to recently isn’t too upset about the cancellation of freshers’ week (“I’m sure we will have plenty of fun on the sly”), but says it is “demoralising to have worked so hard and be paying so much for this ‘world-class education’ via Zoom”. She is resigned to a compromised first year, but hopes it will improve afterwards.

The students applying for university next year have to submit their applications by 15 October if they are applying to study medicine, veterinary science, dentistry, or want to go to Oxford or Cambridge. Many have missed out on a huge chunk of lessons, particularly at state schools. There are well-founded fears that students at private schools and those with private tutors will have an even greater advantage this year. A study by UCL’s Institute of Education found that while 31% of private schools provided four or more live online lessons per day during lockdown, that was the case for only 6% of state schools.

Eren says he now wonders about all the other state schools that don’t send many or any students to Oxbridge. A couple of times he told me about his old school in Croydon, an underperforming comprehensive. His old school mates have struggled to get the places they wanted. “If you go to a school that hasn’t given you all the opportunities that you can have, it’s going to be way harder for you,” he says. “I think there’s a loss of talent and intelligence. It’s just a waste of people.”