England’s biggest teaching union has accused the government of breaking its promise to provide a modest cash boost to every school in England, claiming figures reveal that nearly 5,000 schools have received no extra funds or have even had their funding cut.

In the wake of mounting concern among teachers and parents about a school budget crisis, the education secretary, Damian Hinds, told MPs last year that a new national funding formula would guarantee each school “at least a small cash increase”, a pledge repeated by the prime minister in the Commons last May.

The National Education Union argued the offer was inadequate given the scale of the school funding squeeze, but its analysis of recent government figures subsequently revealed that 4,819 schools had either received no extra funds or had had their budget cut.

“This is yet another failure and another broken promise by government on school funding,” said Kevin Courtney, NEU joint general secretary. “The fact remains that schools were never going to manage on the money promised by government.

“However, headteachers, teachers, school staff and parents will be dismayed that even the meagre amounts of funds supposedly allocated to schools will not be received by everyone. Parents and school staff simply cannot trust what the government says on education funding.”

The NEU compared the schools block funding allocations for 2017-18 and 2018-19 and found that a quarter of primary schools (25%) and one in six secondary schools (17%) either received no cash increase or suffered an actual cut to their funding.

Responding to the NEU analysis, a Department for Education (DfE) spokesperson said that since 2017 the government had given every local authority more money for every pupil in every school in order to ensure fairer funding across the country.

“Government provides this money to local authorities and they have the freedom to work with schools to allocate their budgets in a way that best suits local needs,” the spokesperson said.

“While there is more money going into our schools than ever before, we do recognise the budgeting challenges schools face and that we are asking them to do more. That’s why we’re supporting schools and headteachers, and their local authorities, to make the most of every pound.”

According to the Institute for Fiscal Studies, total school spending per pupil in England has fallen by about 8% in real terms between 2009-10 and 2017-18.

While schools have been struggling to meet rising costs, many local authorities have been forced to divert money from the main schools funding block they receive from the government to their high needs budget in order to meet growing demand for special educational needs support – a move that has to be sanctioned by the DfE.

The shadow education secretary, Angela Rayner, said Labour would end funding cuts and increase per-pupil funding. “The Tories have cut billions of pounds from our schools, which have seen their budgets falling for the first time in a generation,” she said.

“With rising pressure on class sizes and teachers leaving in droves, a generation of children is paying the price for Tory failure.”