The founder of the Leon restaurant chain and co-architect of the government’s school food programme has urged ministers to tackle “holiday hunger” faced by hundreds of thousands of children from low-income families who struggle to eat healthily outside term time.

John Vincent said children living in poverty dropped further behind their better-off peers when schools closed and they had no access to free school meals, and they were often physically and mentally unprepared for learning when they returned. In a Guardian interview, Vincent said: “There’s enough anecdotal evidence to say that some children come back to school less well nourished and generally in less good shape [than when they left], and they go backwards academically.”

Campaigners say children whose families experience financial pressures are not only at greater risk of food insecurity, family stress, isolation and poor health during the holidays, but they also miss out on the so-called social “enrichment activities” such as trips and sporting and cultural activities enjoyed by better-off children.

Vincent, who persuaded ministers to fund a £1.2bn universal free school meals plan last year, said the development of food and leisure schemes during holiday times was the “next stage” in the battle to tackle pupil hunger and address a widening gap in academic attainment between rich and poor children.

Vincent called for schools and local charities, councils and businesses to work together to develop “food-based holiday schemes” which would guarantee children a free healthy meal and a range of activities. “The primary aim is that no child goes hungry, but it is also about enrichment and opportunity for children to do creative things during the holiday.”

However, campaigners warned that ministers had to tackle the underlying cause of the problem. The Child Poverty Action Group said low wages, insecure employment, welfare cuts and unemployment, together with rising food and energy prices, meant many low-income families “could not afford the basics”.

The Trussell Trust food bank network said it believed holiday hunger was behind an 11% spike in referrals of families with children to its food banks during the six-week holidays this summer. It said some of its members extended their opening hours during school holidays to cope with the extra demand for food parcels.

Carmel McConnell, the founder of Magic Breakfast, a charity which works with more than 440 school breakfast schemes, said in extreme cases children had been hospitalised after suffering from malnutrition during long school holidays.

“We have a lot of kids who survive [in the holidays] on the £1 chicken box, and who live on crisps or anything they can get. The teachers tell me it takes about a month to get them back to where they were before the school holidays in terms of their digestive system, their hair, their skin, their teeth. They have real health problems.”

Caroline Wolhuter, who runs a holiday hunger scheme called Holiday Kitchen in the West Midlands, said for children from families under financial pressure school holidays also meant the disappearance of routine opportunities to socialise and engage in active play, as well as putting them at risk of food poverty and poor health.

Wolhuter, head of social inclusion at Ashram housing association, said: “What we see is happening through a landscape of austerity. It’s not just about benefit cuts, it’s about funding cuts and the hollowing out of the labour market. We have a lot more people on low incomes and working families living below the breadline.”

Vincent’s intervention comes days after ministers were warned by the coalition’s social mobility and child poverty tsar, Alan Milburn, that the impact of austerity measures and low pay would see Britain’s poorest children left stranded on the wrong side of a “permanently divided nation”.

Vincent, together with his business partner Henry Dimbleby, was commissioned by the former education secretary Michael Gove in 2012 to write the School Food Plan. It was published last year, and although its main recommendation that all primary school children in England be provided with free school lunches was not accepted in full, it led directly to the introduction in September of universal free school meals for five- to seven-year-olds.

Vincent praised the government for the way it had embraced the school food plan, which he said would help boost pupil wellbeing and academic attainment, he said. However, he was concerned that the nutritional benefits which accrued to poorer pupils during term time were undermined when school kitchens closed outside term time.

He said: “It’s a chance for everybody to think about the next stage of the problem, which is holiday hunger.”

Ministers were told by an all-party group of MPs and peers earlier this year that tackling holiday hunger was crucial if the government was to meet its obligation to end child poverty by 2020. They warned in a paper published in April that holiday hunger “could be having a substantial impact on the developmental needs of children”.

Labour MP Sharon Hodgson, who chairs the all-party parliamentary group on school food, said: “John Vincent is right that we need to have a debate as a country about how we ensure that all the good work schools do during term time, especially with our most vulnerable children, isn’t undone in the holidays.”

The Children’s Society pointed out that an estimated 500,000 UK children living below the bread line did not qualify for free school meals because their parents were in work, but were unable to afford to pay for a decent lunch.

Alison Garnham, chief executive of Child Poverty Action Group said: “We can put a stop to hunger among UK children but it needs urgent action from politicians of all parties to tackle these problems at the root.”

A government spokesperson said: “Our reforms are improving the lives of some of the poorest families in our communities. Universal Infant Free School meals will ensure that 1.5 million pupils are receiving a free nutritious meal every school day, helping them do better in school, eat healthily and saving families up to £400 a year.”