They claim the money is needed to stabilise the education service and ensure that Labour keeps its key election pledge to reduce the size of primary classes.
The drive to raise standards, they say, will also be hit if there is insufficient money for the teachers' pay bill. They are urging that next year's pay rise be linked to inflation - an extra Pounds 500m, or the equivalent of the cost of the Millennium Dome project backed by Tony Blair.
The Department for Education and Employment is thought to be planning to ask the School Teachers' Review Body on pay to create a more flexible pay scale in a radical review. The DFEE has been warned that headteachers must be paid more if they take on failing schools and that the creation of new "superteacher" grades must be backed up with money.
Chancellor Gordon Brown has hinted that he is prepared to ease his tough spending restrictions to provide more money for schools, but he is thought unlikely to do this in next week's Budget. Treasury and DFEE sources said it would be at least a year before savings from social security, as a result of the welfare-to-work measures, could be transferred to education.
Graham Lane, education chair of the Local Government Association, warned that without the extra money the education service would slip into chaos, and added: "We won't be able to do anything about class size. We have got to be able to stabilise the education service, otherwise there will be Armageddon."
An estimated 55,200 additional pupils are expected in schools from September, so class sizes will inevitably rise unless extra teachers are taken on.
This year the overall pupil:teacher ratio, at 18.7:1, is already 0.4 worse than it was in 1995, the year parents and governors took to the streets in their thousands to protest about education cuts. The Institute of Public Finance already estimates that an additional 2,400 teachers will be needed if classes for five, six and seven-year-olds are to be cut to 30 or under pupils.
Local authorities are also spending Pounds 656m above the Government estimate of what should be spent on education (the standard spending assessment).
On top of the demand for an inflation-linked pay award for teachers local authorities say they need to spend a further Pounds 427m - Pounds 137m of which will pay for increased pupil numbers. Councils also forecast the need for spending on capital to increase from Pounds 442m to Pounds 1,172m to start addressing the current backlog of essential work in schools.
They insist that the Government should fully fund the 1998 teachers' pay award, claiming the decision to phase this year's increase has left them with a Pounds 92m problem before even the start of the next financial year.
Last year an estimated 5,000 teachers lost their jobs and although staging the redundancies may have limited the impact for one year, the problem will catch up.
Local authorities have blamed some schools for exacerbating the problem by squirrelling away cash. While councils have raided their own reserves to protect schools from the worst effects of cuts, heads and governors have stashed away an estimated Pounds 600m in reserves. But Mr Lane said: "We are not proposing that individual school balances are raided to pay teachers. "
Schools have also tended to spend more on support staff. DFEE figures show that since 1991 spending per pupil has increased from Pounds 1,199 to Pounds 1,329, an 11 per cent increase, while spending on support staff has increased from Pounds 121 to Pounds 175, a rise of 45 per cent.
Earlier this year the Association of Teachers and Lecturers reported a 63 per cent increase in the number of classroom assistants employed between 1991 and 1994, with numbers jumping from 13,641 to 21,914. At the same time, the number of primary teachers fell from 176,295 to 175,270.
Latest figures from the DFEE and local authorities for 199596 shows a 22 per cent reduction in spending on discretionary awards compared with the previous year, a 3 per cent reduction in spending on the youth service and cuts in adult education.
Leader, page 20