Schools in some of England’s most deprived areas will suffer increased budget pressures and cuts next year, despite the government’s promise of extra funding, according to analysis by teaching unions.

A report into individual school allocations for 2020-21 – using data released by the Department for Education – found “a strong link between deprivation and the scale of government cuts to school funding”, even accounting for the £2.6bn increase announced in August.

The analysis conducted by the National Education Union (NEU) found that real-terms cuts to schools serving the poorest pupils would be more than three times as deep as those in schools in the wealthiest areas.

“We are not being churlish, we are just stating the facts,” said Geoff Barton, the general secretary of the Association of School and College Leaders, which represents many secondary school heads in England. “The extra money for schools is not enough to reverse the cuts and the funding crisis is not over.”

Nine out of 10 secondary schools with the highest proportion of pupils on free school meals will lose out, with average real-terms spending cuts of £509 per pupil compared with 2015-16, while the majority of those serving the least deprived will be £117 worse off than five years earlier.

About 40% of primary schools with the highest levels of pupils eligible for free school meals will experience further cuts, averaging from £300 to £380 per pupil less than in 2015-16.

The cuts come despite the government’s plan to put more money into schools, starting in 2020-21 and continuing until 2022-23, when it says an additional £7bn will be spent on mainstream schooling and special educational needs and disabilities (Send) combined.

Paul Whiteman, the general secretary of the National Association of Head Teachers, said one in three schools would only receive increases of about 1.8% in their overall funding, which amounts to real-terms cuts after inflation.

“This shows that it will take a lot more than the government is currently offering in order to properly restore the funding that’s been lost over the past several years,” he said.

Kevin Courtney, the joint general secretary of the National Education Union, said: “The unfairness of the distribution of Boris Johnson’s additional school funding is breathtaking. Johnson promised that there would be no more ‘winners and losers’ in education – a noble commitment, but it does not match reality.”

Lord Agnew, the schools minister in the House of Lords, came under fire from state school heads at a conference in Newcastle, with one telling Agnew that the new funding was “going to support children who are in more Conservative areas of the country” rather than disadvantaged areas such as the north-east of England.

Agnew dismissed the criticism as “political noise” and reiterated the government’s determination to raise minimum per pupil funding to £5,000 for secondary schools.

Earlier analysis by the Sunday Times found that more than 90% of the schools receiving a funding increase of more than £100 per pupil will be in Conservative-held constituencies, in areas such as Essex and Kent.

The new figures from the DfE show that schools in the most deprived parts of England, including Tower Hamlets in London and Hartlepool in the north-east, will face above-average levels of cuts.

Angela Rayner, the shadow education secretary, said the figures showed the government’s promises on school funding were “rapidly unravelling”.

“Schools in more affluent, Conservative areas and those attending selective grammar schools are set to benefit, while pupils and schools in disadvantaged areas will continue to lose out, entrenching, not tackling, inequality,” Rayner said.