Local authorities have lodged more than 200 appeals with the Department for Education for permission to move away from the national school funding formula next year, Tes can reveal.
In at least six cases, the requests have been made against the wishes of local headteachers.
The new formula is being introduced from 2018-19 in an attempt to allocate funding to schools according to a single set of principles.
But the DfE has received at least 202 appeals from local authorities that want to deviate from these rules, Tes has learned.
A headteachers union is warning that the calls to subvert the formula are caused by a shortage of funding and will force schools to wait longer to receive the money they are owed under the new national system.
Mary Bousted, joint general secretary of the NEU teaching union, said: "The fact that so many local authorities requested to be able to move their funding into high needs shows that there isn't enough money to go round.
"It's clear that there isn't enough money in the national funding formula, and the schools that will suffer most are those with the most challenging intakes."
A new rule brought in with the introduction of the national formula limits the extent to which local authorities can prop up budgets for pupils with "high needs" with money taken from their main schools funding pot, known as the "schools block".
They can still transfer up to 0.5 per cent of their schools block funding to support high needs budgets – but only with the agreement of schools forums.
But, if schools forums do not agree to the transfer, or if a local authority wants to move more than 0.5 per cent, permission is needed from the education secretary.
Latest figures show that 58 local authorities have asked to divert cash into their high needs pot against the wishes of local headteachers, or beyond the levels permitted under the formula – although 19 requests have since been withdrawn.
The figures are revealed in a written answer by schools minister Nick Gibb, in answer to a query from Liberal Democrat home affairs spokesman Ed Davey.
Historically, many areas have only managed to keep their high-needs budgets afloat with large amounts of "schools block" cash.
'Caught in a squeeze'
Malcolm Trobe, deputy general secretary at the ASCL school leaders' union, said the funding requests showed that schools and local authorities were "caught between a rock and a hard place".
He said: "We understand the pressures are there in high needs. However, the issue is the government isn't putting enough money into the high needs budget, which means local authorities are caught in a squeeze.
"We certainly don't want to see schools having money in their [main schools budget] taken away for other purposes, nor do we want to see pupils with high needs suffer because there isn't the level of funding to support them."
Mr Trobe said one of the reasons for limiting the amount of local flexibility over funding was to ensure schools moved as quickly as possible onto the national formula.
"If you're taking money away from the [schools block] then there's less money to distribute, and it will slow the process down," he added.
As well as asking to transfer money between different funding pots, local authorities can request to change the "minimum funding guarantee" set out under the national funding formula, which is meant to ensure that no school sees its funding drop by more than 1.5 per cent.
They can also ask for funding to take account of falling pupil numbers or "exceptional" factors – such as a school's listed building status, or the existence of a school farm.
The DfE has revealed, in correspondence with Ed Davey's office seen by Tes, that as of 7 December 2017 there were 202 requests in total from local authorities that did not want to hand out cash to schools in strict accordance with the national formula.
It has not provided a full breakdown of what the 202 requests relate to, but names Kingston-Upon-Thames, Bromley, Middlesbrough, Hackney, Dorset and Bath and North East Somerset as areas that submitted requests to transfer high needs funding without the approval of their schools forum.
Dr Bousted said the funding squeeze would "create tensions at a local level", she said, with local authorities forced to make tough decisions.
She added: "There are also going to be tensions within multi-academy trusts. If they don't divvy the money out according to the national funding formula, I think there will be problems."
The government had originally planned for the formula to end the role played by local authorities in setting school budgets. However, this would have required legislation, which could have been difficult to get through parliament following last year's general election result.
A DfE spokesman said: "Councils have always been able to adapt their funding formula to meet local needs, as long as they adhere to strict criteria set by the government.
“We are investing an additional £1.3billion in school and high needs funding. We have protected the high needs budget in real terms over the next two years and, under the new national funding formula, every local authority will see an increase.”