Boris Johnson’s pledge to “level up” pupil funding in English schools will benefit grammar schools and those in more affluent areas, while schools serving the most disadvantaged communities will miss out, a report claims.

The new prime minister has promised to ensure that “historically underfunded” schools will see an uplift, and that there will be an increase in minimum levels of per pupil funding, from £3,500 to £4,000 in primaries, and from £4,800 to £5,000 in secondaries.

He has pledged to reverse the real-terms education cuts, which have led to schools closing early and redundancies among teaching staff, with a total increase of £4.6bn funding per year by 2022/23.

The report, by the Education Policy Institute (EPI), however, finds that schools with less challenging pupils who have fewer additional needs, will stand to benefit most, while those teaching children with low prior attainment and those for whom English is not their first language, will gain less.

According to the EPI “almost all” schools serving the most disadvantaged communities would miss out on additional funding. By contrast, primary schools with the least disadvantaged pupils, where fewer than 5% are eligible for free school meals (FSM), would receive an average increase of £271 per pupil.

Nearly all of England’s 163 grammar schools stand to benefit from Johnson’s commitment; they would pick up, on average, an additional £130,000, the EPI said. The average non-disadvantaged pupil stands to gain £116 extra a year – more than double the £56 the average pupil eligible for FSM attracts.

Concern has also been raised about the prime minister’s failure to address the crisis in special educational needs and disabilities (Send) funding and provision.

John Biggs, the Labour mayor for Tower Hamlets, in east London, has written to Johnson warning that “a tipping point” had been reached.

He wrote: “We face a national crisis in special needs provision, as the funding we get from government isn’t keeping up with the number of children and young people who rely on these vital services, leaving a gap that councils have to fill.

“This gap has been growing and we have now reached a tipping point, with very serious implications for the future. There was much talk about school funding during the Tory leadership campaign, and I urge Boris Johnson to immediately review the situation and provide additional funding to help fill the gap.”

Johnson’s decision to focus initially on levelling up funding is aimed at pacifying Tory MPs on the backbenches who have become increasingly vociferous about what they regard as unfair funding, in which schools in disadvantaged areas of London attract significantly more money those in rural areas.

EPI’s deputy head of research, Jon Andrews, said: “The prime minister’s drive to level up school funding implies that funding should be equal despite the fact that children’s circumstances and opportunities are anything but. This approach would disproportionately direct additional funding towards the least disadvantaged schools with the least challenging intakes, at a time when progress in closing the attainment gap has stalled and may be about to go into reverse.”

The shadow education secretary, Angela Rayner, said: “Schools across England have been hit by years of Tory cuts and need investment to give every child the best possible start in life, not just a lucky few. The last prime minister failed to end austerity and it’s clear the new one won’t do any better.”

Critics have complained that Johnson’s £4.6bn per annum pledge is nowhere near enough, or that there needs to be more detail on when the money would be available, and for what exactly.

A Department for Education spokesperson said: “The prime minister has made clear that we will increase minimum levels of per pupil funding in primary and secondary schools and return education funding to previous levels. We will be announcing more details in due course and, until then, any assumptions are purely speculative.”