Local Schools Information, the local authority-backed advisory body, said that generously funded GM schools would suffer.

It claimed the pressure for a national formula for the sector came from schools in low-spending areas, and said that Government was to blame for funding differences.

“It is ministers, rather than local councillors, who are responsible for most of the disparity in funding between similar schools in different areas - as well as what is widely perceived as an inadequate level of funding.

“The present exercise of consultation over a discussion paper on a national funding formula for GM schools appears to be little more than an elaborate smokescreen to disguise this fact,” it added.

Heads of opted-out schools have long pressed ministers to standardise funding, but many believe that it would be wrong to limit a national formula to the 1,100-strong sector.

The Grant-Maintained Schools Advisory Committee said opted-out schools were generally strongly in favour of a national funding formula and believed it should be introduced sooner rather than later.

It added: “Many feel that the issue is one for the whole maintained sector, rather than for GM schools alone.”

Up to now the Government has shied away from introducing a national system because it would produce winners and losers, but John Major believes that it is the way forward in the long term.

Civil servants have, however, warned that some schools could lose up to 22 per cent of budgets while others could gain as much as 17 per cent, with large differentials within individual authorities.

The GMSAC said opted-out schools not covered by the common funding formula - now operating in 23 areas - already felt vulnerable.

It added: “The problem of winners and losers is recognised, but there are winners and losers already with the present funding mechanisms and the general view is that this can be overcome satisfactorily by the introduction of sound transitional arrangements.”

LSI claimed the discussion paper on a national funding formula for GM schools, which contains an element of payment-by-results, was fundamentally flawed.

It added: “There is a real danger that the present proposal to try and tinker with one aspect of the system in isolation could produce serious consequences elsewhere with no appropriate opportunity to assess the overall impact. ”