Headteachers are querying the cost-effectiveness of a policy they fear will use money meant for IT or even staff

Come September, children at Mudeford infants school in Dorset are not going to be getting hot school dinners. They'll be eating sandwiches. Somewhere along the troubled history of the coalition's policy to give all infant children a free school meal, the requirement for food to be hot quietly disappeared, to the relief of some headteachers.

"With declining budgets we just don't have the finances to employ the staff to serve hot meals," Mudeford's head, Duncan Churchill, explains. "We'll get the money for the actual food, but no extra money to run it. And I'm not going to make teaching assistants redundant in order to employ serving staff."

Some school leaders argue that the proposed sum of £2.30 a child being paid by the government will buy a hot meal – but not what is needed to supply it. Churchill's choice highlights a dilemma. If it's not enough, where do schools get the money to fund this new legal requirement for free meals?

Ministers have recently woken up to the fact that heads are saying they'll have to spend teaching and learning money to cook and serve meals, supervise lunches in newly equipped dining halls, clear up and dispose of the waste.

Churchill runs through the figures. "For the food element we'll get £50k. It would have cost us another £10k a year to staff hot dinners. With sandwiches, there are still significant costs: I've been quoted £10k for an external cold room to keep the dinners fresh when they come in. The local authority gave me a capital grant of just over £4k. So I now have to find £6k to buy this fridge."

That money will have to come from Churchill's capital budget (money he'd planned to use for ICT equipment) and from his school development budget – that's staffing, textbooks and anything else children need in class. He's not happy about it. "£56k is being spent to give children a sandwich," he says. "Give me £56k to spend in other ways and I could transform the educational chances of children at this school."

According to Liberal Democrat peer Lord Ashdown, up to 10% of schools will not be able to deliver universal free school meals by September, and so will be breaking the law.

The evidence that heads are using money intended for children's education to pay for dinners has escalated a poisonous feud that's been brewing at the heart of the coalition since Conservative critics first alleged that the Lib Dems' policy was underfunded and poorly planned. Last week it was reported to be on a "red flag" list of policies likely to fail.

Michael Gove appears unhappy at the prospect of education budgets being used to pay for the initiative. "I am sure that you will agree with me that we must not risk forcing schools to subsidise meals by reducing their spending on teaching and learning," the education secretary wrote to the Treasury in November. "I would be grateful for your assurance that my budget will be increased to fully cover the cost of this new commitment, as I am unable to fill any shortfall." Last week, however, he declared himself fully behind the policy.

With around 40 school days left until the free dinner bell rings, heads are finding their own ways of coping.

Education Guardian has been following progress at St Mary Redcliffe primary in Bristol. The headteacher, Emma Payne, sounds exasperated with the whole affair. Her school needs a £65,000 kitchen extension to provide meals by September. But so far, no building work has started. She says she is "really hoping not to" have to dip into her teaching and learning money, but is still waiting to hear whether the local authority's capital board will fund the extension. Until she hears, Payne won't know if her budget's safe for next year, or whether she'll have to sacrifice a whopping chunk of it.

Meanwhile, some have hatched ingenious plans. "We've had to be creative," says Stuart Renshaw, executive principal of five primaries that make up the Saints' Way academy trust in Cornwall. To serve high quality hot meals, he explains, two of his small schools require significant investment: one needs a larger kitchen, the other needs a new servery with a vegetable preparation and cooking area. The idea is to run the kitchen as a business in the evenings, offering takeaways to parents in an area that has few restaurants or local shops. His hope is that the profit will subsidise the extra costs involved. These now include the salary of a catering manager responsible for implementing the detail across all five schools. Renshaw will also need significant uptake of hot dinners from older pupils to have a chance of breaking even.

The small schools he's in charge of at least benefit from a ring-fenced allowance of £3,000 apiece from central government. His largest primary, St Petroc's, won't get an additional penny beyond the allocated £2.30 a meal.

Here, he'll have to reconfigure the school hall and buy more kitchen and dining kit. It's costing him £13k – and it's the school's capital budget that's taking the strain. Weren't academies given the chance to bid for grants to pay for these kinds of cost? "The window for accessing that academy money was about two weeks in January," Renshaw says dryly, "and nobody was told about it."

Junior school governor and blogger Andy Jolley is aghast that schools' capital funding, or any money intended for education, could be spent on the Lib Dems' free school meal policy. "Does Gove agree with the policy given he must now know schools have to make cuts to fund it?" he asks.

Not all heads are dismayed at the prospect of using teaching and learning money for free meals. Aaron Meredith, executive head of Marine Academy primary and Ernesettle Community primary in Plymouth, says he's already had to spend – "hundreds, not thousands" – on tables and chairs. And while he's sure there will be ongoing costs "I'm happy to absorb them". And how? "It could come from the pupil premium," he says. "Or from the staffing budget."

At Payhembury primary in Devon, which is part of the small school pilot that gets advice and support to implement free school meals, headteacher Penny Hammett says she is keeping an open mind. She doesn't run a school dinner service at the moment, so has to start from scratch. If only the 30 children entitled to free meals take them, she'll be running in deficit. "As a small school, I'll have to use my protected £3k, and after that it would have to come from school budgets," she says.

She needs 40 of her 70 pupils to take school dinners to stand a chance of breaking even. "But if you get 40 children out of a total of 70 having dinners and that leads to a deficit of £1,000 a year, you might decide that the benefits of so many having a quality hot lunch make it worth doing," says Hammett. "There's so much I can't predict."

Headteachers' goodwill towards the idea of free school meals for all infants – and the goodwill is evident – has been strained by the arguments between politicians and the chaos many perceive in its implementation.

"Education policy and strategy is like trying to stand on a water bed – there is no firm footing, and at the chalk face we have to manage as best we can," says Renshaw. "I think it's a fantastic idea. It needed another two to three years of careful planning."

At St Mary Redcliffe, Payne is just frustrated at the time and energy she has to expend. "If there's no building going on here by September, I will talk to my school dinner provider and we will work out a solution," she says. But currently, she has other things on her plate. "I've got a massive child protection situation that's just ballooned and an urgent building project that has to be prioritised for safety reasons. The new kitchen – well, it will happen or it won't, but you know, the kids will be fed."

• This article was amended on 20 May 2014. An earlier version said there seemed to be agreement among school leaders that the proposed sum of £2.30 a child being paid by the government would buy a hot meal – but not what was needed to supply it. That has been amended to say that some school leaders argue that is the case.