Ministers are looking at plans to change the way schools are funded. One option is to reduce the amount of money allocated on a per-pupil basis, allowing more cash to be distributed according to need.
This would be the first challenge to the competitive market in education which was at the heart of Tory policy for more than a decade.
The idea, raised by council leaders at a meeting with David Blunkett, the Education and Employment Secretary, and minister Stephen Byers, would allow extra cash to be spent on pupils with special needs and on cutting class sizes.
The Conservatives forced schools to compete for pupils and the money they attracted - Pounds 2,286 on average for a secondary pupil and Pounds 1, 687 for primary children.
The new proposal, from the Local Government Association, would cut the proportion of cash allocated to schools on a per-pupil basis from the present 80 per cent to 70 per cent. Targeting the additional 10 per cent of cash strictly according to need would also limit the amount heads and governors can save - schools have Pounds 600 million squirrelled away while authorities face huge cuts.
The overall pot of money for education in an authority would remain the same but individual schools could lose under the new formula. It would be up to councils to decide how to spend the extra money.
A senior Scottish Labour source said Brian Wilson, the Scottish education minister, realised that phasing out assisted places would not raise enough cash for the massive school rebuilding programme which would be needed if class sizes were cut.
A Government source would not comment on the proposal, but said: "We are looking at ways of increasing delegation and getting more money to schools. "
Graham Lane, education chair of the LGA, said: "Changing this formula would create a much more flexible system - we want funding to be targeted more on need.
"The whole idea of the market place is a barmy way of running education. It is a false view that schools should be regarded as customers based on the market."
The Government is committed to a review of local management of schools.