Labour’s plan to provide free school meals for all primary school children and pay for it by levying VAT on fees at private schools has a great deal to recommend it. It is clear and uncomplicated and sends a strong message about what a future Labour government would look like: in favour of good universal provision and against privilege for a small minority. This is exactly the territory that Theresa May has shown signs of hoping to colonise, and it was significant that she did not criticise the proposal at the launch of the Conservatives’ local election campaign. For Jeremy Corbyn and his team, this is a hit.

There is solid evidence that good nutrition improves academic outcomes. In 2008, Labour piloted the idea in the London borough of Newham and in Durham where free dinners throughout primary were introduced. An evaluation published by the Department for Education in 2012 found that more pupils were likely to have free school dinners if they were offered to everyone, and that there was a “significant positive effect” on attainment at key stages 1 and 2, which was particularly marked in children from less affluent families. The policy was adopted across England in 2012, by the Liberal Democrats, who pushed the coalition government into providing free school meals for children aged between four and seven, which they saw as a first instalment in their manifesto commitment to universal primary provision.

The first question is whether it is worth ensuring that every child has a nutritionally balanced meal in the middle of the day. The answer is yes. The harder question is whether it is the best way to spend a significant amount of money – £1.5bn, Labour reckons, will be raised from putting 20% VAT on school fees.

The evaluation suggested it was more effective in raising standards than the “Every Child a Reader” campaign. But there are always hard choices to make about where to spend scarce resources. The former chief inspector of Ofsted, Michael Wilshaw, who backed levying VAT on school fees (like the former education secretary Michael Gove), told the BBC that expanding the pupil premium might be better value for money. And value for money really counts: with spending frozen and costs such as the national living wage and pension contributions rising, England’s schools are facing real cuts in their budgets of up to 8% for the first time in recent memory. They even have to pay the new apprenticeship levy, which the cross-party public accounts committee estimates takes another 0.4% off budgets.

Yet the government has chosen this moment to introduce what the Institute for Fiscal Studies describes as the biggest change in the system of funding for a generation. The new national funding formula will move a shrinking budget around between different schools. Some will be slightly better off, many much worse. None will feel more financially secure by 2020 than in 2015, least of all in London. The intention of making funding more equitable is sensible, but introducing such a big change when budgets are already stretched to breaking point will leave some schools as much as 17% worse off. Unsurprisingly there is mutiny, not least among Tory backbenchers, who are lining up to beg Mrs May to delay. Meanwhile, the prime minister is also determined to expand free schools and spread grammars despite the lack of evidence that they raise standards.

Taken together, warns the PAC, the impact of the cuts will be so severe, and the DfE’s capacity for monitoring the fragmented system so weak, that there is a real risk to the quality of education.

At their weekly confrontation across the dispatch box, the prime minister has repeatedly floundered in the face of Jeremy Corbyn’s challenge on cuts to school budgets. It has been his most successful line of attack, and her reluctance to answer both in the Commons, and at her press conference on Wednesday shows that she is aware of how weak the government’s position is. Strikingly, there are rumours that Tory policy wonks are thinking along the same lines as Labour. This is a plan that is unequivocal in its clarity, in an area where the government is really struggling. It is a copybook exercise from the manual of effective opposition.