The policy would let heads run their own admissions, pay, discipline and uniform policies. It would effectively mean the end of local education authorities.

Tory councillors have already urged party leader William Hague to tone down the policy by making it optional for schools. Teacher unions plan to use the conference to argue that the scheme, in its present form, would be unworkable.

John Dunford general secretary of the Secondary Heads Association, said the policy could lead to the “disintegration of the state school system” unless the party agreed to have bodies separate from schools responsible for admissions and school places.

However, at the Scottish Tory conference in June, delegates were almost unanimous in their backing for the policy.

Other issues to be covered in fringe conference debates include school funding and the teacher recruitment crisis.

The conference runs from October 2 to 5.