Hundreds of millions of pounds must be pumped into schools, including those in Sheffield, to ensure they do not lose out under new funding plans, council bosses have warned.
Schools in England are already facing a squeeze on budgets, and many are set to lose out further under Government plans to introduce a new national funding formula, according to London Councils and Core Cities UK.
The groups, which represent local authorities in the capital as well as other major cities, including Sheffield, are calling for an extra £335 million a year to be invested in England's schools to make sure that the new funding formula can be introduced without any schools facing a cut in money.
There are concerns that continued school budget pressures will affect the quality of education children receive, as well as depriving local businesses of skilled employees and in turn damaging the economy, the groups said.
The Government said the new formula will end a 'postcode lottery' in school funding.
But in a letter to Education Secretary Justine Greening, Judith Blake, leader of Leeds City Council and chairman of Core Cities UK, said: "Despite protections on school funding, school spending per pupil has already faced reductions in real terms in many of our schools and the National Audit Office predicts that it is likely to fall by eight per cent by 2020.
"Our city schools are already dealing with unprecedented rising demand for places, high levels of in-year pupil mobility and increasing challenges around teacher retention and recruitment.
"We have very real concerns about how some of our schools will be able to cope with further considerable cuts in funding resulting from the introduction of the national funding formula. Any loss of funding could jeopardise the ability of schools to continue to deliver good educational outcomes and put pupils' longer term employment prospects at risk."
The proposed new national funding formula announced by Ms Greening in December increases money targeted at schools with additional needs, including deprivation.
The changes, introduced from 2018 to 2019, will mean more than 10,000 schools gaining funding, it has been suggested.
But teaching unions have warned that 98 per cent of schools face a real terms reduction in funding for every pupil over the next few years due to ongoing funding pressures, with an average loss of £339 per primary pupil and £477 for secondary students.