Last month, the government announced a £4bn package of investment for schools until 2022/23, as part of its latest spending review. This includes £700m extra for children with special educational needs and disabilities (SEND) for 2020/21.
But the IFS says the increase, of £4.3bn in real terms, will only reverse a reduction of eight per cent in spending per pupil since 2009, which it describes as "an unprecedented period without growth".
The government has also pledged an extra £300m in spending on further education for next year.
However, the IFS says that this leaves colleges and sixth forms £1.1bn short of what they need to even reverse cuts since 2010.
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"The 2019 Spending Round provided genuinely substantial increases in school funding, enough to more or less offset all cuts since 2009. Of course, that still means no real growth in spending per pupil over a 13-year period," said IFS research fellow Luke Sibieta.
"The extra £300m for further education and sixth forms provides for a small rise in 2020, but at least a further £1.1bn would be required to fully reverse cuts since 2010."
Early years spending is also looked at, which found that the proportion spent on low-income families has reduced, from 45 per cent of total government spending on early years to 27 per cent. The government's spending review pledges an extra £66m for government childcare.
IFS research economist Christine Farquharson, added: "The Spending Round's announcement of £65m (in real terms) for the early years will certainly be welcome in the sector, but won't affect the big changes that have taken place in how the government supports childcare in England.
"Big rises in the early years budget in recent years seem to have been focused more on supporting families with childcare costs rather than providing early education. With at least eight different childcare support programmes in operation today, the government needs to be clearer about its goals for the early years."
The extra money for early years has been branded "unacceptable and tokenistic" by childcare leaders.
Also coming under scrutiny is the extent to which children's social care spending has become increasingly focused on responding to crisis, rather than on offering early help.
Spending on looked-after children by the government has increased by 20 per cent since 2010, while total spending on children's social care is up nine per cent.
Over the same period, children's centre spending is down by 62 per cent and youth services funding is down by 65 per cent.
The research has been commissioned by the Nuffield Foundation, which is particularly concerned about the impact of further education cuts on disadvantaged young people.
"While we welcome the additional investment in schools, the failure to fully reverse the cuts to further education remains a concern for the half of 18-year-olds who do not go to university and who are, on average, already less advantaged than those who do," said Nuffield Foundation chief executive Tim Gardem.
A Department for Education spokesperson said: "We recently announced a £14bn investment in schools - the biggest cash boost for a decade, which the independent IFS has said will restore schools' funding to previous levels in real terms per pupil by 2022/23.
"Alongside this, we announced a significant real-terms increase in funding for 16- to 19-year-olds in 2020/21 to make sure we can continue to develop world-class education to rival countries on the continent. We also provided £700m extra for children with special educational needs and disabilities.
"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."