Priscilla Chadwick, chair of HMC, will reignite the debate about vouchers - which would give parents the same amount to spend on private fees as it costs to fund a state school place - at the association’s annual conference.

“There has been a great deal of co-operation between independent and state schools recently,” she told The TES.

“I am delighted that much of the good practice pioneered in the independent sector is now being adopted by schools in the state, but inevitably the Government could be doing more towards this.

“Certainly, the education and political landscape has changed so much that we should be reconsidering the issue around vouchers.”

But her calls are unlikely to win support from the Government, which axed assisted places - which provided fee subsidies from the state for underprivileged children at private schools - shortly after Labour came to power.

This week Ruth Kelly, the Education Secretary, pulled out of an appearance at HMC, which represents 240 leading private schools, at the De Vere Belfry hotel in Warwickshire. Geoff Lucas, HMC general secretary, said officials failed to give a reason for her absence.

“It was disappointing,” he said. “I cannot be sure what she was going to raise at the conference, but if she was only going to talk about fizzy drinks most members would not have missed her presence anyway.”

Jacqui Smith, schools minister, will take Ms Kelly’s place.