Policy-makers on the Labour and Liberal Democrat-controlled county council this week agreed to set an overall budget for the authority of Pounds 408m - Pounds 6m above the level approved by ministers.
The move, expected to be confirmed by the full council later this month, will need Government approval. It comes despite claims by the Education and Employment Secretary Gillian Shephard that councils will have enough cash in the next financial year to avoid teacher redundancies and keep down class sizes.
It could be followed by other Labour and Liberal Democrat councils who will try to pin the blame for any cuts in school services on the Government. With the local government elections in May, possibly crucial to the future of John Major's Government, ministers are expected to try to blame profligate councils for excessive increases in council tax.
All of the additional Pounds 6m planned by Cambridgeshire is intended for frontline services. The bulk will go to schools but Pounds 800,000 has been earmarked for social services. The authority said none of the cash would be kept back for central administration.
Six local education authorities - Devon, Gloucestershire, Shropshire, Newcastle, Sheffield and Barnsley - had spending limits capped by Government in 1995-96 despite widespread protests from parents and governors.
Only Somerset had its cap relaxed after John Gummer, the Environment Secretary, said the county had shown that school budgets would otherwise be cut.
Mrs Shephard has won an extra Pounds 774m for schools for the new financial year and ministers appeared confident that it would be enough to prevent further teacher redundancies and to counteract rising class sizes.
But authorities are already claiming it is not enough and that they will have to make major cuts - and education which accounts for the lion's share of their budgets will once again be in the firing line.
Despite the proposal in Cambridgeshire to put Pounds 5m more into schools, other education services will almost certainly have to be cut.
Community education is looking at a loss of Pounds 2m and learning and behaviour support services could also be hit.
Last month headteachers in Wolverhampton told Mrs Shephard that the health and welfare of their pupils was in jeopardy because of underfunding.
Calling for an urgent review of the provisional budget from Government for the authority, they stated: "The present chronic underfunding is already blighting the lifetime prospects of Wolverhampton children. Unless there is substantial additional support for spending on essential services by Wolverhampton Council, it will not only be the educational entitlement, but also the health and welfare of pupils in this borough, which will be put at risk."
This month's decision on the pay award for teachers could make a major difference to local authorities budgets.
Mrs Shephard is understood to have told the teachers' pay review body that it needs to consider the wider implications of any settlement. Last year schools faced difficulties when councils could not fully fund the 2.9 per cent award.
Cambridgeshire has budgeted for a 2.75 per cent rise for teachers this year. Kent said it was looking at a 3.5 per cent rise.