Giving state schools freedom from government control is the key to raising standards to levels achieved by independent schools, according to a study commissioned by the body that represents the heads of Britain's elite private schools.
International comparisons show that schools with more autonomy perform better, regardless of their socio-economic background, said Alan Smithers, professor of education at Buckingham University, author of the research.
Heads and teachers should be allowed to choose how to teach without interference, said Professor Smithers. All schools should also be allowed to pay more money to teachers if they are struggling to recruit in difficult areas.
His research, co-authored by Pamela Robinson, also of Buckingham University, was presented to leading independent school heads of the Headmasters' and Headmistresses' Conference, which represents 250 private schools including Winchester, Eton and Harrow. HMC schools get better results than state grammar schools, despite the fact that grammars have a more selective intake, according to the study.
Independent schools also take a similar number of pupils eligible for free school meals as the country's top 200 comprehensives, said Professor Smithers.
"The thing that makes the difference seems to be the independence the schools enjoy," he said. "It is important because it suggests ways the state system could be improved."
He said there was no solid evidence that the smaller class sizes typically found in private schools had a significant impact on results.
He also drew on international studies, saying that results from the Programme for International Student Assessment (Pisa) tests pointed to greater success for schools free of government interference, fee-charging or not.
"In independent schools, teachers and heads emphasise that teaching and learning decisions can be taken close to the classroom," said Professor Smithers.
"State school teachers always have to respond to directives and initiatives coming from the centre.
"The sensible thing would be for the Government to step back and let people steeped in teaching and learning make things happen."
Professor Smithers said he was not ruling out the impact that selecting pupils from well-off backgrounds has on independent schools' results, but he said that did not tell the whole story.
There should be guaranteed minimum pay for teachers, but beyond that schools should be allowed to pay more money to attract the best staff if they need to, as is the case with private schools.
His comments were criticised by Chris Keates, general secretary of the NASUWT, who said it was "risible" to hold up independent schools as the example for state schools to follow.
"It is nonsense to say that all independent schools have high standards," she said. "There are lots where parents are paying money under false pretences.
"We do want to see more professional autonomy for teachers, but we want that changed within the state system."
Professor Smithers' research also drew attention to the subjects studied at A-level, with independent schools more likely to do "hard" A-levels including further maths and economics.
HMC results were better in 24 out of 30 subjects compared to grammar schools and in 29 compared to comprehensives and academies. The one subject where state schools did better was sociology.
Elsewhere at the conference, held in London, the rebel Labour MP Frank Field lambasted both the independent and state sectors in education. He told the private school heads that their stance in public life was unacceptable and accused them of "standing aloof".
They should be doing much more to help state schools by sharing their expertise and backing academies, he said.
But Mr Field also criticised the quality of state education, saying it was a "national catastrophe".
He said state schools were weighed down by "decades of failure" and that they should be setting a target for 95 per cent of children to achieve five good GCSEs including English and maths.
He told the heads: "Part of the reason you face such pressure is because so much of the state sector is so poor."