The Government, headteachers said, is failing to embrace the independent sector, refusing to fund their partnership projects and is marching head-on towards examination meltdown, with scant regard for curriculum reforms led by private schools. This was the frustration, articulated by Sir Eric Anderson, the former head of Eton College and a cornerstone of the Headmasters’ and Headmistresses’ Conference (HMC) representing 260 of the UK and Ireland’s top private schools. Sir Eric, who has taught Prince Charles, Mr Blair and David Cameron and appeared in Labour’s teacher recruitment campaign “No one forgets a good teacher”, told the private-school gathering: “If Britain knows how to run the best (independent) schools in the world, why are we not also running the best state schools in the world?

“It is not because there are not good students in these state schools; nor is it because there are not good teachers. There are. Some of the best students I met at Oxford and some of the best teachers I have ever come across were at state schools.

“Why then? I think, after all these years, I know the answer. It is because political ideology has prevented the country from learning important lessons from the independent schools.”

So just how would the education world look if state schools started to talk to their independent brothers and sisters a little more? Andrew Boggis, this year’s chairman of HMC and head of the pound;11,300-a-year Forest school in north-east London, criticised ministers for spending seemingly pathetic amounts on the official programme to “build bridges” between the sectors. The Pounds 1.4 million per year invested in the independent-state school partnership, he said, was “only slightly more than the furniture allowance for the Learning and Skills Council”.

Although he lauded the project’s aims, Mr Boggis said the private school brand was being “hijacked” and insisted ministers should commit serious sums to allow, among other things, independent teachers to take state pupils in shortage subjects, such as science and languages.

More claims that the government was tinkering were made by Sir Eric, who was returning to the conference 12 years after retiring from Eton. He stopped short of advocating a return to the 11-plus, but asked why the Government allowed selection by aptitude - specialist schools can choose 10 per cent of their pupils on potential for music, languages or sport - but not academic ability?

“Specialist selection, schools of choice, could give us a proper chance against the emerging economic powers,” he said. “Nothing can be done unless the government considers selection and schools of choice.”