Marcus Rashford and a group of celebrity chefs and campaigners have called on Boris Johnson to review the government's free school meals policy.
The group, including Jamie Oliver, Hugh Fearnley-Whittingstall and Tom Kerridge, have written to the PM asking him to "fix" the system long-term.
They called for a strategy to help "end child food poverty" before the summer holidays.
No 10 said "no child will ever go hungry" because of the Covid pandemic.
The call for a wide review comes after another row over free school meals during February half-term.
The government has said food will be provided to children by councils under the Covid Winter Grant Scheme while schools are closed for the holiday.
Councils and unions say the government should provide food vouchers instead, with the Local Government Association's Councillor Richard Watts telling BBC Radio 4's PM programme the grant had already been allocated for other support.
But Transport Secretary Grant Shapps told BBC Radio 4's Today programme: "We are down to semantics whether it is the school delivering the meal or whether it is the local authority - fortunately there is quite a lot of different support available."
As well as getting the backing of Rashford - who has led campaigns around child poverty over the course of the pandemic - the letter has been signed by chefs Oliver, Kerridge and Fearnley-Whittingstall, along with actor Dame Emma Thompson and over 40 charities and education leaders.
Organised by the Food Foundation charity, the letter said it was time to "step back and review the policy in more depth".
They called for an "urgent comprehensive review into free school meal policy across the UK" to feed into the government's next Spending Review, saying it should look at:
- the threshold for being eligible for free school meals
- funding - including whether the current allowance is enough
- how schools can be helped to provide the best quality meals
- the impact of Covid on children in low-income families
- making sure there is no stigma
The signatories praised the Department for Education's "swift response" to reports earlier this week of inadequate food parcels sent to families, saying the "robustness of the message from you and the secretary of state on this issue was very welcome".
But, they added that "following the series of problems which have arisen over school food vouchers, holiday provision and food parcels since the start of the pandemic", now was the time for a review.
Anna Taylor, executive director of the Food Foundation charity, said the last few months had seen "crisis after crisis with the provision of free school meals".
"The result of that is disadvantaged children have often paid the price," she told BBC Radio 4's Today programme.
"Our view is that really unless we do a root and branch review these problems are going to still keep appearing."
Chef Fearnley-Whittingstall also called for a more consistent, long-term response to the issue of food poverty.
"We need to get out of this fire-fighting, highly reactive series of actions by the government," he told the same programme.
'Vital next step'
The signatories want a review to be published and debated in Parliament before the 2021 summer holidays.
"We are ready and willing to support your government in whatever way we can to make this review a reality and to help develop a set of recommendations that everyone can support," the letter said.
"School food is essential in supporting the health and learning of our most disadvantaged children.
"Now, at a time when children have missed months of in-school learning and the pandemic has reminded us of the importance of our health, this is a vital next step."
Anti-poverty campaigner and food writer Jack Monroe welcomed the letter to the PM, but told the BBC: "We need to be feeding children right now."
She added: "While it is great to be looking longer term... having an underpinning strategy that means that children aren't put into poverty in the first place, we need to also immediately be putting resources in to ensure people aren't going hungry, today, tonight, next week and in the February half-term.
"This isn't a rhetorical thing. It isn't a dinner party discussion. We need to be doing this now."
A Downing Street spokesperson said: "It is great that celebrities and groups across society see the importance of school food. The PM thanks Marcus Rashford for his letter and will reply soon.
"School food is essential in supporting the health and learning of the most disadvantaged pupils. The prime minister has been clear that no child will ever go hungry as a result of the pandemic".