English schools face a budget cut of an estimated 10% in real terms during the next parliament if the Conservatives win the election after David Cameron conceded that his party could not promise to inflation-proof education funding.

Schools would have to pay 5% more to fund rising teachers’ pension and national insurance contributions, while economists said the prime minister’s admission would mean a further cut in real terms.

Cameron initially sought to dress up the funding pledge as a “flat cash per pupil” deal, because the amount of money following each child would remain unchanged. Speaking at Kingsmead school in Enfield, north London on Monday, he added: “So I can tell you, with a Conservative government, the amount of money following your child into school will not be cut.”

But when questioned, Cameron conceded that the funding would not rise in real terms, prompting educationalists and political opponents to complain about the impact. Over the past five years, the education budget has been protected from cuts, rising in line with prices. “I accept that that is a difficult decision for some schools because the amount of cash per child is not going up by inflation, the amount of cash is staying the same,” he said.

The prime minister did say that there would be some rise in overall school funding because the number of pupils in schools was increasing.

But the Institute for Fiscal Studies economic thinktank said the real-terms budgets would be eroded in the next parliament because they were not inflation-proofed. The impact would amount to a 7% fall in real terms.

The IFS added that employers’ pension contributions for teachers had increased by 2%. Employers’ national insurance contributions were also going up because of the introduction of the single-tier pension, which would cost schools an extra 3%.

Economists said it was not possible to simply add together all the cuts, but it was estimated that they would amount to a 10% real-terms cut to the schools budget for England over the lifetime of the next parliament.

Luke Sibieta, the thinktank’s education programme director, said: “The schools budget was ringfenced in the 2010 spending review and the 2013 spending round. The net result is that spending per pupil will have risen 1% in real terms over this parliament.

“What David Cameron has proposed is a flat cash per pupil settlement for the next parliament which, in terms of resources per pupil, would be quite a big difference compared with the previous parliament. The real value of spending will be eroded over the next parliament.”

Peter Kent, a serving headmaster and president of the Association of School and College Leaders, said school leaders shared the prime minister’s commitment to raising standards, “but we’ve got to have the resources to provide the quality of education he is talking about. We can’t make bricks out of straw, we’ve got to have the resources.”

Kent, who is head of Lawrence Sheriff school in Rugby, said headteachers were already concerned about budgets, even before Cameron’s speech.

“There are bound to be cost of living pay rises and all of these are going to impact significantly on our budgets – never mind what happens to inflation. Even before this announcement, schools were saying to us they were really concerned about their budgets.”

The shadow education minister, Tristram Hunt, said Conservative claims to be protecting school budgets were unravelling. “David Cameron has been forced to admit that his plans will see a real-terms cut to spending on schools,” Hunt said. “The truth is that you can’t protect schools when you have plans to take spending as a share of GDP back to levels not seen since the 1930s.”

Labour has not yet announced its plans for financing school budgets.

The Liberal Democrats said the Conservatives’ spending plans would lead to cuts to unprotected areas of the education budget – such as funding for nurseries and colleges – of £3.1bn a year by 2020.

The party also said that David Cameron’s announcement also raises questions over the future of the £2.5bn pupil premium, which is money targeted at the most disadvantaged students to close the attainment gap. A Conservative party spokesman said on Monday that the party had no plans to scrap the scheme.

Russell Hobby, the general secretary of the school leaders’ union, the NAHT, warned of a “harsh, austere” period ahead and estimated that the impact on the schools budget would be larger, at about 12% in real terms by 2020. “That is a significant sum of money, especially at a time when external services to schools have been cut to the bone already. School leaders will need to prepare for a harsh, austere climate. Staffing is the biggest cost a school faces. This will be protected to the last, but what happens then?”

Martin Doel, the chief executive of the Association of Colleges, said that while Cameron’s speech offered some protection to schools, it was “desperately disappointing” for sixth form and further education colleges, which educate more than 830,000 people aged 16 to 18. “This leaves college students extremely vulnerable to huge cuts in the next parliament,” he added.will nevertheless put pressure on unprotected areas of government spending, such as local government and the police, if the Conservatives are returned to office.

Cameron said: “Good school places need money and we will make sure our schools are properly funded. Today, I can make this commitment about Conservative plans. We’ve demonstrated in the past five years that we can protect the schools budget while reducing the deficit and we will do so again.

“So I can tell you, with a Conservative government, the amount of money following your child into the school will not be cut. In Treasury speak, flat cash per pupil.

“And as the number of pupils in our schools is going up, that means the amount of money going into our schools will do so too.”Cameron said that although funding per pupil would not go up by inflation, schools had demonstrated that they could “be more efficient, more effective and they can make their budgets work”.

The prime minister added: “They can particularly make their budgets work because many now have greater freedoms and abilities to run the schools the way they see fit.” is, frankly, not good enough.

“So this is what we’re doing. We are waging war on mediocrity. We are saying no more sink schools and no more bog-standard schools either.”

Before Cameron’s speech, the education secretary, Nicky Morgan, had given the impression that she had secured a commitment that the schools budget would be protected in real terms, but it appears the consequences for other departments, such as the Home Office and Defence, had made this impossible.