But heads in independent schools have broadly welcomed the plans to give parents a “pupil passport” - expected to be worth around pound;3,500 a year - saying it could help them to broaden their pupil intakes.

Parents would be allowed to spend the money on state-run, voluntary or independent schools, but would not be able to add to the sum themselves.

Tim Yeo, Conservative education spokesman, said the plans would result in the abolition of catchment areas, which would allow children to attend some of the country’s top-performing schools, wherever they lived.

“Our proposals would, for the first time, give real choice to parents regardless of their social or economic background,” he said.

The Conservative party says the changes would mean that popular schools would receive extra funding and expand while unpopular schools would be forced to make improvements.

The Tories had planned to introduce pupil passports only in urban areas.

But now they will introduce the scheme across the country if they win the next general election, expected next year.

John Dunford, general secretary of the Secondary Heads Association, said the pupil passport was completely unworkable.

“Some schools would flourish, but it would damage children’s life chances in other schools and the education system as a whole,” he said.

But the Independent Schools Council said its members were encouraged by the proposal, although they wanted more details of the passport system.

Only 45 prep schools and five senior schools out of 1,300 affiliated to the ISC charge less than pound;4,500 a year.

But heads of more expensive schools said they might open a select number of places to the passport system, then top up the fees themselves from bursaries.

Kevin Riley, headteacher of the pound;7,000-a-year Bristol Cathedral school, said: “In principle, the passports would be an attractive way to widen access. The fear would be that, like assisted places, they could be scrapped when the political wind changed.”