It found itself at the centre of a political storm after helping to deliver Unicef UK’s first ever food aid programme for struggling families in Britain – now the charity, which had never given out out a single food parcel and never intended to, has delivered its one millionth Breakfast Box.

“We had absolutely no idea of the level of need,” said Stephanie Slater, the founder of School Food Matters. The charity was preparing a school meals nutrition project in south London when lockdown came. With its plans on hold, it switched to distributing food parcels to families local schools had identified as vulnerable.

In its first week, the charity handed out 500 boxes filled with fresh fruit, cereal, bread, rice and milk. By week 10 it was giving out 5,000 boxes. Schools that initially said they did not need the help changed their minds. By its January peak, the impromptu project was distributing 9,000 boxes a week – equivalent to 91,000 breakfasts.

To anyone involved locally it was clear this was a major crisis. And yet it was the £25,000 School Food Matters received last autumn from the UN children’s agency to part-fund the programme (the bulk of the £1.3m spent on the scheme came from Impact on Urban Health, part of the Guy’s and St Thomas’ charity) that triggered a media furore.

In December the Tory minister Jacob Rees-Mogg described the £700,000 Covid food support programme from Unicef UK as a “political stunt of the lowest order”. The House of Commons leader praised the government’s child poverty record and said the UN children’s agency “should be ashamed of itself”.

Rees-Mogg implied food poverty was not really a problem in the UK, and accused Unicef UK of “playing politics … when it is meant to be looking after people in the poorest, the most deprived countries in the world, where people are starving, where there are famines and there are civil wars”.

The resulting media attention, amplified by social media, has left the charities and schools involved wary of commenting on the row. Asked whether the phenomenal demand for breakfast boxes had vindicated Unicef UK’s intervention, Slater said: “We just responded to what we saw before us.”

Katie, a mother of three at Belham primary school, Southwark, said the boxes were a lifeline. People who did not have kids at home, or had not experienced a drastic cut in income, may not understand why, she said. Her work dried up, but she did not qualify for self-employed income support assistance. “Of course it [the food aid] was needed. It was definitely needed. And a lot of people appreciated it.”

What School Food Matters would say was that the past 12 months had been no ordinary tale of urban hardship. The astonishing demand for its Breakfast Boxes revealed hidden depths of food insecurity and financial precariousness that pre-dated the pandemic.

It was not just the already struggling who were going without, but the “newly hungry”, poleaxed by overnight income loss. For schools, the formal indicators of deprivation used to work out their funding needs were no longer an accurate measure of the hardship their communities faced. About a quarter of the families who received Breakfast Boxes did not qualify for free school meals.

James Robinson, the headteacher of Camelot primary school in Southwark, knew the community was deprived. Half of his 387 pupils were eligible for pupil premium funding help because of low incomes. Yet this did not tell the whole story, he realised. More than 250 – two-thirds of his pupils – needed food aid through the School Food Matters scheme.

He hired a van, and with friends delivered the bulky Breakfast Boxes to families, clocking up 30,000 steps before the school day started. On local housing estates he talked to parents. He was met with warmth and generosity, and saw desperate poverty and overcrowding. His trips, even for someone who had worked for years in this community, were revelatory.

He discovered families had spent weeks without income while waiting for a universal credit benefit payment. There were 28 children in his school with migrant worker parents who, he realised, were ineligible for official support because of “no recourse to public funds” rules; 35 of his families were homeless and living in temporary housing. All were going hungry.

Alison Sprakes, the assistant headteacher at Belham primary school, in a relatively affluent area of the borough, saw a similar phenomenon. Fewer than one in 10 pupils qualified for pupil premium funding. Yet by May, 45 families needed Breakfast Boxes. “We had families who on the face of its look relatively affluent, but when you dig deeper, that’s not the case.”

Part of the answer, said Slater, was to expand eligibility for free school meals to more pupils (Southwark is one of a handful of councils that offer universal free school meals). For Robinson, the deprivation data, on which school funding is based, needs overhauling. “Not enough people from my world understand this world is on our doorstep,” he said.

After Easter, the scheme ends. Slater is hopeful that the return of school Breakfast Clubs and the possibility that the economy will pick up will mean it is not too badly missed. Robinson was not so sure: “We could continue this all summer. There’s no indication things are going to get better for many of our families.”