The IFS has analysed the cost of potential commitments on schools and education spending made by all the Conservative leadership hopefuls.
It particularly highlighted Johnson's claim that some areas of London receive per pupil funding of about £6,800, while other parts of England receive about £4,200 per pupil. The MP for Uxbridge and South Ruislip and former Mayor of London branded this a "postcode lottery".
However, the IFS analysis points out that a new national schools funding formula in England was introduced in April 2018, which allocates funds to local authorities based on need and costs.
"With the introduction of this formula, the government - which Mr Johnson was part of - effectively ended a long-standing postcode lottery in school funding in England," the report states.
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While there are still differences in per pupil funding, this is because local authorities receive higher funding for areas with greater levels of deprivation and/or because they have to pay London weighting.
"Policymakers who want to reduce differences in funding between areas should be clear that doing so would almost certainly reduce the extent of extra funding for deprivation and/or London weighting," the IFS states.
Many of the remaining contenders to become Conservative Party leader and the next Prime Minister have said they would reverse past cuts to education or maintain current spending. However, to do this would cost billions, the IFS has calculated.
Per pupil funding directly allocated to schools in England fell by four per cent in real terms between 2015/16 and 2017/18, while total school spending per pupil - incorporating sixth form funding and local authority spending - fell by eight per cent in real terms between 2009/10 and 2017/18.
To reverse these cuts would cost £1.8bn and £3.8bn respectively.
In addition, a further £1.1bn would be needed each year up until 2023 to maintain spending in real terms, taking rising costs into account.
If a similar boost were to be given to 16-19 education providers, reversing four per cent of cuts would cost about £230m, while reversing cuts of eight per cent would cost about £480m.
With a Spending Review on the horizon, the IFS noted that current government plans imply a £2.5bn reduction in departmental spending outside of health between 2019/20 and 2022/23. Therefore, extra schools or education spending could only be funded through deeper cuts to other areas of spending, higher taxes or higher borrowing.
The Department for Education spokesperson said: "Since 2017, we have given every local authority more money for every pupil in every school, while allocating the biggest increases to the schools that have been most underfunded.
"While there is more money going into our schools than ever before we know schools face budgeting challenges, which is why we have introduced a wide range of support to help schools reduce costs and get the best value from their resources - from a free-to-use vacancy service to cut the costs of recruiting teachers, to advisors who are providing expert help and support to individual schools that need it.
"The Secretary of State has made clear that as we approach the next spending review, he will back head teachers to have the resources they need to deliver a world class education in the years ahead."
