Jacob Rees-Mogg and Nicky Morgan among those supporting Frank Field’s proposals to help poorer children who may go hungry

More than a dozen Conservative MPs have publicly backed a Labour MP’s bill to provide free meals to poorer children who may go hungry in the holidays because of the absence of school lunches.

High-profile Tories supporting the backbench bill include the treasury select committee chair Nicky Morgan and the chair of the 1922 committee of Conservative MPs, Graham Brady.

The 14 Tory MPs who have signed, out of 113 members in total, come from the right and left of the party and include former cabinet minister Oliver Letwin as well as Jacob Rees-Mogg, Caroline Spelman and Zac Goldsmith. Labour, Green, Scottish National party and Liberal Democrat MPs have also signed.

The veteran Labour MP Frank Field, who is chair of the all-party parliamentary group (APPG) on hunger, will present the bill on the first day back from summer recess. It would place a legal duty on local authorities to ensure the provision of free meals and activities.

Figures from the Trussell Trust food bank network show a significant rise in the number of food parcels being provided to children over the summer months, with 67,506 three-day emergency food supplies distributed in July and August 2016, compared with 63,094 in the previous months – an increase of more than 4,000. Just under half of those children were of primary school age, the charity’s research showed.

An APPG report into hunger in school holidays found about 3 million children were at risk of going without meals during the summer, with the loss of free school meals for two months adding between £30 and £40 a week to parents’ outgoings for one child.

Field, who also chairs the work and pensions select committee, said the government could raise £41.5m for the scheme by ringfencing 10p from every pound raised from the sugar tax on soft drinks, though £315m from that tax has gone to the Department for Education to address school funding shortages.

Brady said he was convinced of the bill’s merit because it would not put an extra burden on local authority funding. “I don’t see any reason not to support the bill, because very sensible Frank has looked at how it might be funded, and so certainly at the very least it is an interesting idea that merits further discussion,” he said.

Field said he hoped the backing of more than 100 MPs would give the government the impetus to back the bill.

“If the prime minister were to pick up this bill and run with it, at nil extra cost to the government, she would tackle overnight one of the great injustices afflicting children in this country – a widening of inequalities at school caused by a lack of food during the holidays,” he said. “Likewise she would immediately be cutting off one of the main supply routes to food banks.”

Field’s bill is unlikely to succeed without backing from government departments or Conservative whips. He will attempt to secure the legislation using a “presentation bill” – a kind of private member’s bill proposed by backbenchers.

However, the Speaker will allocate limited time for backbench MPs to present bills, and Field’s chances may have been scuppered by Conservative MPs Peter Bone and Christopher Chope. The pair camped out for four days before the summer recess to flood the list with 73 separate presentation bills, including scrapping international aid and making the UK’s exit from the EU an annual bank holiday.

Field’s bill will be given a date for debate only after the Speaker has allocated time for each of the 73 proposed by the pair, with 13 days allocated between now and November 2018 for debating any type of private member’s bill.

Presentation bills usually have a slim chance of becoming law because another type of private member’s bill is allocated to 20 other MPs through a ballot – with guaranteed time for debate. Any bill where the debate goes on past 2.30pm on a Friday also automatically fails.

However, private members’ bills have succeeded when the government gives support. Earlier this year, the Conservative MP Bob Blackman won backing for his bill to oblige councils to prevent the homelessness of anyone, regardless of their status, within 56 days, with the communities secretary, Sajid Javid, pledging £48m in extra funding.

• This article was amended on 1 September 2017 to remove Mel Stride’s name as a supporter of the bill. Stride’s name was included in error in the original press release.