Labour has called for an urgent inquiry into the way A-level results were awarded last year, after reports that private schools in England gave out more than eight times as many top grades compared with before the Covid pandemic.

The government scrapped exams in England in 2021 and told teachers to award A-level and GCSE results by assessment, but figures collected by the Sunday Times suggest some schools took undue advantage by massively increasing the rate of top grades awarded to their pupils.

A staff member at a school identified as one of the worst offenders told the Guardian that teachers felt pressurised into awarding the highest grades, while the school’s leaders orchestrated internal assessments to show evidence if queried by Ofqual, the exam regulator, or the exam boards tasked with overseeing the process.

School leaders also told teachers who complained about the ethics of inflating grades that the exams boards had given “a nod and a wink” to the practice, and that schools were “all doing it”.

In one case of alleged grade inflation, Derby high school went from 6.5% of its entries awarded A* by examination in 2019 to nearly 54% awarded by assessment in 2021. North London Collegiate, a private girls school, nearly trebled the rate of A*s awarded so that more than 90% of its entries were assessed as A*s.

The shadow education secretary, Bridget Phillipson, said: “Ministers’ chaotic, last-minute decision-making created a grading system which enabled privileged schools to push sky high results unchallenged.

“Reports that teachers were pressurised to put up grades show utterly unacceptable behaviour in some schools. An inquiry is urgently needed, including enabling anonymous evidence from staff to uncover how these results went unchecked last summer.

“Young people without adults advocating for them have been let down terribly by a government system that was open to abuse. Ministers must get a grip and get a proper plan in place to stop inequalities widening again this summer.”

Robert Halfon, the Conservative MP who chairs the education committee, supported the call for an inquiry.

An inquiry would probably require the publication of individual school results for A-levels and GCSEs, which the Department for Education (DfE) has so far refused to do.

Prof Lindsey Macmillan, of University College London’s Institute of Education, said the DfE should allow researchers access to school and pupil data to enable them to study the 2021 results.

An experienced teacher at a private school who spoke to the Guardian said the pressure to increase grades came from senior leaders, rather than from parents.

“If you went against it, you met with a few different responses, some of it just stonewalling, others were that ‘exam boards know this is going on, it’s a bit of a nudge, nudge, wink, wink, they know we’re doing this, we know that they know’, it was all a bit chummy.

“The other response was ‘other schools are doing the same, so we are just doing what other schools are doing’. But teachers know other teachers from other schools so we were able to compare and know that this was definitely not going on in other schools.

“Although we were aware that private schools were more corrupt in their dealings than state schools, there was a spectrum within private schools that we were aware of as teachers.

“Many teachers felt very uncomfortable with it, but many felt they couldn’t say anything. Teachers said to me they felt very uncomfortable, and I felt there was nothing we could [do] that wouldn’t unleash a whole load of hell upon our heads, in terms of intimidation or making our lives difficult in a number of ways.”

A DfE spokesperson said: “Overall results in 2021 showed success for young people who were targeting top grades from all types of schools and from all backgrounds. The grades achieved reflected the hard work of students and their teachers, and those efforts should not be undermined.

“We are clear that exams are the best form of assessment, which is why they will take place this summer with adaptations to maximise fairness for young people.”

Ofqual said in a statement: “All school types awarded higher A-level grades last year, when teachers determined their students’ grades, than they did in 2020. All heads of schools and colleges submitted a formal declaration on the accuracy and integrity of grades and processes supporting them.”

The rapid increase in overall grades awarded last year – after the abrupt decision to scrap exams when England went into lockdown in January – was first highlighted last August when A-level results were published.

The national figures showed that 70% of all A-level grades awarded to private school pupils were A or A*. In comprehensives the figure was just 39%.

When the use of teacher assessment was announced by the then education secretary, Gavin Williamson, experts predicted that A-level grades would rise even further than they did in 2020, when exams were also scrapped.

Derby high school did not respond to a request for comment.