Thousands of headteachers across England are writing to parents to warn that there is “simply not enough money in the system” to fund schools properly, as their costs continue to rise and budgets come under severe pressure.

The letter from more than 4,000 heads will tell around a million families that the government’s new national funding formula still means their children face an unfair “postcode lottery”, with some schools able to afford class sizes of 20 but similar schools in other regions forced to have classes of 35 pupils.

The heads argue that the proposed national formula – designed to iron out historic disparities in funding – will do little to solve the funding crisis affecting many state schools.

“The finances of very low-funded schools are still insufficient to provide the service that your child needs,” the letter, due to be sent on Thursday to parents of children in 17 counties, will say.

“Parents and carers need to be clear that schools in very similar socioeconomic areas will continue to have entirely different levels of funding. This often amounts to hundreds of thousands of pounds in the primary sector and even millions of pounds across the secondary sector. Far from being resolved, your child’s education will still be at the behest of a postcode funding lottery.”

Calculations done by the heads found that – despite the promise by the education secretary, Justine Greening, of £1.3bn extra cash – the proposal amounts to a real-terms cut of 4.6% by 2020 compared with five years earlier.

Simon Murch, a teacher in Sheffield, said most schools still faced real-terms budget cuts and were struggling to keep up with rising costs. “What this means in Sheffield is that lots of schools are looking to restructure and teaching assistant posts are being lost. Some schools are not putting salaries up. There is a lot of scrabbling around trying to find ways of saving money,” Murch said.

The letter includes analysis of government statistics that reveal a secondary school in York would get an average of £4,700 per pupil in 2018-19, compared with £6,450 for a pupil in Greenwich, London – nearly £2.5m a year less for a school with 1,400 students. Second worst off among secondary schools were those in Barnsley, where schools get an average of £4,729 per pupil, followed by Leicester, with £4,730.

A spokesperson for the Department for Education (DfE) said: “The national funding formula – backed by £1.3bn of investment – will mean that for the first time school funding will be distributed according to a formula based on the individual needs and characteristics of every school in the country.” The DfE underlined that no schools would lose funding as a result of the formula.

Earlier this month, Greening told MPs the new formula was a historic reform that would “represent the biggest improvement in the school funding system for decades”. The formula aims to end the uneven funding through local authorities that has resulted in some schools – particularly in inner London – receiving thousands of pounds more per pupil than other areas.

Local authorities use different formulas to distribute funding in their area. For example, a secondary school pupil with low previous results would attract £2,000 in extra funding in Birmingham, compared with just £36 in Darlington.

The headteachers concede that the new formula will improve funding for schools that are currently the worst off, but argue that Greening’s reforms would still uphold huge disparities in school budgets across the country.

“A school in a disadvantaged area of Crawley or a tough part of Barnsley will receive millions of pounds less than schools from similar socioeconomic areas in London or Manchester,” said Jules White, head at Tanbridge House school in West Sussex, who coordinated the letter.

The headteachers are urging parents to lobby their MPs for improved funding, following similar campaigns from heads at the end of the last school year, and from schools and unions during the runup to the election.

Rob Corbett, the principal of Ifield community college in Crawley, West Sussex, and one of the signatories to the letter, said he had been forced to make cuts worth £350,000 in recent years, and described the new funding formula as a “political fudge”. “If we do not get substantially increased funding, our ability to support the range of needs of our students becomes significantly reduced,” he said.

“Our students take the same GCSEs as others in the country and we are judged by the same Ofsted framework, but we are supposed to do this for far less money per student, which seems wrong to me.”

Labour’s Angela Rayner, the shadow education secretary, said the letter showed the government was still not giving schools the resources they needed. “There is no new money and every penny has been found by cutting the education budget elsewhere,” she said.

John Tomsett, the headteacher of Huntington school in York, said that while the city still had relatively low funding, schools in York benefited more than any other local authority from the new formula’s increase in base funding. However, he said the formula “should not be about redistributing the same-sized pot. Instead, the pot needs to get bigger.”

Catharine Darnton, the headteacher of Gillotts secondary school in Oxfordshire, said: “This is a very difficult time to introduce a national funding formula because the overall amount of funding for schools is simply inadequate. Small increases in funding through a new formula will nowhere near offset even one year’s cost pressures in many schools.”

The headteachers put the inconsistencies in funding down to the fact that how much a school gains or loses is dependent on caps. “The caps are largely arbitrary and mean that any new per pupil funding is often based on the previously discredited formula,” the letter says.

Since Greening’s announcement, a cascade of data has suggested that the funding changes will do little to lift the underlying budget pressures facing schools.

A parliamentary question tabled by Layla Moran, the Liberal Democrat education spokeswoman, found that more than one in three schools in England ran an operating deficit last year, with hundreds of schools having dipped into their reserves for three or four years in a row.

Meanwhile, the education unions updated their campaigning website School Cuts to include the new national formula, and found that nearly nine out of 10 schools would see cuts in real terms by 2020.

According to the unions’ calculations, a typical primary school will be worse off annually by £52,546, and a typical secondary school will have lost £178,000 each year since 2015.