Mr Clarke is preparing to announce new education plans

But local education authorities had a "very, very important role" and he could not envisage centralised funding.

His comments followed a report that the education authorities (LEAs) might be cut out of the funding process.

The Local Government Association chairman, Sir Sandy Bruce-Lockhart, said councils had not been informed of any plans to limit their role.

And the association's education chairman, Graham Lane, said many schools would be worse off.

Direct funding

Mr Clarke will be spelling out the government's new five-year plan for education on Thursday.

But giving evidence to the MPs' committee, he said LEAs would continue to allocate resources to schools, help those that were struggling and provide "strategic leadership" for the local education service.

He did not think it feasible to have a system under which 26,000 schools were funded directly by the Department for Education and Skills (DfES).

"The idea that the DfES could press a button here and stick it out there I think is the wrong view."

But he said: "What I do think is we want to achieve certainty in funding regimes.

"That does require some changes in the balance of the relationship."

Tweaking

Graham Lane told BBC News Online that local and national government needed to share responsibility for the funding system, to ensure fairness.

Mr Lane was wary of commenting on speculation ahead of the formal announcement of the plans on Thursday.

But he said: "If they are going to strengthen the ring-fencing of the central government grant going to school budgets, that's one thing.

"But if it's going to affect the way local government can tweak the distribution so schools in more need get more money, that's quite another.

"I hope it's the former."

The more funding was driven from the centre, the more simplified the system had to be.

"We do need transparency and fairness but you can't have simplicity with those two," he said.

'Foolish step'

Local Government Association figures suggest councils added to the government's provision for education this year with an additional �185m - enough, it says, to pay for 6,000 teachers.

Graham Lane said many LEAs topped up the amount ministers intended schools to have from what they raised through the council tax, diverted from other areas or bid for from central grants.

"If you cut out local government from a share of the responsibility, you are cutting out access to that money as well.

"If they did that, that would be a very foolish step," he said.

Arguments between national and local government over the funding of schools are nothing new.

At the height of the school budget crisis in 2003, ministers were suggesting a large part of the problem was LEAs' withholding money they should be passing on.

But Charles Clarke later admitted Whitehall had got its sums wrong - and promised a guaranteed rise in the funding per pupil of at least 4% for this year.