A major pledge to boost school coffers will reverse recent budget cuts - but leave schools where they were 13 years ago, according to a respected economic thinktank.

Ministers announced plans to invest an extra £7.1 billion in schools in England over three years from next year.

But an Institute for Fiscal Studies (IFS) report published today says that after inflation is taken into account, schools will only be getting an extra £4.3 billion per year in real terms by 2022-23.

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And while the funding is enough to almost reverse the real-terms cuts in schools budgets since 2009-10, there has still been a 13-year real-terms freeze on schools’ budgets, which is “an unprecedented period without growth”.

Luke Sibieta, IFS research fellow and report co-author, said: “No change over a 13-year period is still a very big squeeze on schools.

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“If you’d have told schools that in 13 years’ time, they would be getting exactly the same level of funding, they would naturally be quite concerned.”

Earlier this year, unions calculated that £12.6 billion was needed in extra funding to reverse the cuts and “provide the standard of education that society expects”.

Geoff Barton, general secretary of the Association of School and College Leaders, said the report was “a sober assessment of the government’s hyped-up announcements over education funding”.

“School and college finances will continue to be under pressure despite the increased level of investment,” he said.

Kevin Courtney, joint-general secretary of the NEU teaching union, said: “This IFS report confirms our belief that the additional money announced in the spending round is insufficient.

“They point out that even after the spending round, schools still have to cope with an unprecedented 13-year long funding squeeze.”

Paul Whiteman, general secretary of school leaders’ union the NAHT, said the new funding could “still leave school leaders struggling to make ends meet.”

He said: “The expectations on schools are far more extensive than they used to be, and with fewer resources and services available to them.”

The funding was announced after years of lobbying for cash by unions and headteachers, including a march of 2,000 headteachers’ in Westminster last year.

Headteacher Jules White, coordinator of the WorthLess? school funding campaign, which organised the march, said: “A sum of £14 billion that was trumpeted by the government now turns out to be £4.3 billion over three years in real terms.

“This is important as it takes schools back close to 2010 funding levels but massive shortfalls will still persist in areas such as SEND and post-16 funding.

“At the same time school budgets are still being used to prop up the massive cuts to local authority budgets, which should be there to help our most vulnerable pupils.”

Today’s IFS report was funded by the Nuffield Foundation.

A Department for Education spokesperson said the extra funding was “the biggest cash boost for a decade” and that, alongside extra funding for schools, there was “a significant real-terms increase” in funding for 16- to 19-year-olds, as well as £700 million extra for children with special educational needs and disabilities.

The spokesperson added: “Together, this package will give all young people the same opportunities to succeed and access the education that’s right for them regardless of where they grow up. The prime minister is clear that education is one of his main priorities, and we want a system that boosts productivity, improves social mobility and equips children and adults with the skills and knowledge they need to succeed.”