Official statistics obtained by Labour’s education team show that there were nearly 46,000 appeals by dissatisfied parents in 1993-4 - a rise of 120 per cent on the 1989-90 figure of 21,000. More recent figures are not available but education authorities believe the numbers have continued to rise.

The figures have been seized upon by Labour as evidence that the Government policy of offering parents a greater choice of schools for their children is failing. They have also prompted renewed calls from senior backbench Tories for the Government to take a fresh look at the way school places are allocated and funded.

The rise in appeals is likely to increase pressure on the Prime Minister from the Tory right-wing which wants popular schools to be given the money to expand, a move thought to be opposed by the Treasury because of the cost.

During last summer’s leadership contest, Mr Major suggested that oversubscribed schools in England might be allowed to expand. The idea followed a similar pledge by his opponent John Redwood, who, before resigning as Welsh Secretary, had introduced a Pounds 23 million scheme to provide an extra 1,500 places in 12 schools. Mr Major has yet to expand on his proposals.

In October, a TES survey of Conservative MPs found that admissions was the educational issue which most concerned constituents.

The number of parents appealing to education authorities has risen for five years in a row, producing a total of 173,196 over the period. Of the 45, 876 appeals in 1993-4 only 13,255 were successful.

Mr Byers said that families have been deceived into believing they have more choice than is possible. He said that under Labour, education authorities would draw up plans to co-ordinate the provision of places.

Mr Byers criticised the Government’s inability to produce figures more up-to-date than those for 1993-94. This week’s statistics were only published after a parliamentary question.

Ministers have found it increasingly hard to square the idea of parental choice with the pressure to remove 1 million empty school places.

This week Sir Malcolm Thornton, Conservative chairman of the Commons select committee on education, said talk of choice would remain largely rhetorical if the Government stayed committed to keeping the number of school places as low as possible.

“The problem is that parents do not have an actual choice, only a preference and that preference has to be set in the context of schools that are full. There’s an inconsistency in telling authorities to remove surplus places and, at the same time, having open enrolment. Open enrolment means there has to be some slack in the system.”

He called for a major re-think on school places. The select committee has asked the Government to consider introducing a national funding formula for all schools across Britain. “We need to look at the total issue; tackling one bit at a time produces anomalies.”

David Hart, general secretary of the National Association of Headteachers, warned: “There’s a potential explosion building up between parental choice on the one hand and school authorities on the other.” More heads, he said, have to admit children against their better judgment thanks to the findings of authority appeal panels.

Alan Parker, education officer with the Association of Metropolitan Authorities, said: “The Government’s theory of choice assumes that people want different things. In fact all parents want the best that’s going locally. ” He pointed out that the number of appeals in an area ebbs and flows. Popular schools, for example, eventually get a reputation for rejecting most applications, and parents try elsewhere.

A spokeswoman for the Department of Education and Employment said the publication of the Citizen’s Charter had made parents more aware of their rights. “The vast majority get a place at the school for which they have expressed a preference.”