A cross-party group of more than 100 MPs have written to the prime minister calling for an overhaul of school funding that would boost some schools’ budgets but cut others’ by up to 16 per cent.

The 112 MPs are urging David Cameron to rethink school funding, arguing that the current system is “arbitrary and unfair” and leaves some schools with £2,000 less per pupil than others.

They want the system replaced with a new model that should be “along the lines of” a formula drawn up by the F40 campaign group, which represents currently low-funded areas.

Under the F40 group’s proposed formula, schools in Hackney would lose about 16 per cent of their core budgets. Those in Southwark would lose 13 per cent and those in Greenwich, Lambeth and Tower Hamlets would lose about 12 per cent.

But schools in Barnsley would receive a 10 per cent funding boost and those in Salford an extra 6 per cent. Wokingham, Knowsley and the East Riding of Yorkshire would gain about 5 per cent.

In the letter to Mr Cameron, the MPs say: “It is widely acknowledged that the existing school funding model is a muddle and that funding for individual schools with similar pupil characteristics is arbitrary and unfair.”

They say that schools in the 10 best-funded local authority areas will receive on average £6,297 per pupil this year, while those in the 10 least-funded areas will receive on average £4,208 per pupil.

They write that school funding should be “based on a clear rationale and geared towards improving educational standards across the country”.