Pupils need inspirational teachers, the charity says
Forty-two per cent of the UK's top scientists and scholars were privately educated and the trend looks likely to continue, a report suggests.
A study by the Sutton Trust educational charity looked at the schools and universities attended by 1,700 top scientists and scholars.
It also found 51% of medics, 70% of judges, 54% of leading journalists and 32% of MPs went to independent schools.
The charity says less-privileged children should be given equal chances.
Private schools educate about 7% of children in the UK and about 9% of 17-year-olds. About 14% of university entrants are from independent schools.
In the study, analysts looked at the educational backgrounds of 1,700 of the 2,200 fellows of the Royal Society and British Academy.
They found 56% of the fellows had studied at Oxford or Cambridge universities.
Chairman of the Sutton Trust, Sir Peter Lampl, said: "This report is yet more evidence of the uneven life chances in Britain.
"Students from the independent sector are substantially more likely to reach the top of our most coveted professions and succeed in influential walks of life."
The researchers concluded that the access to research-led universities - where students could go on to become leaders in their field - was "skewed towards those from better-off backgrounds".
They based this finding on recent GCSE, A-level and university entrance data.
"Private school pupils are up to five times more likely to achieve an A* grade at GCSE in core academic subjects and account for more that one third of top grades in key A-levels like physics, chemistry, economics and history", they wrote.
Sir Peter said it should be a priority to provide bright students from poorer homes with the same opportunities as more privileged young people.
"This means giving them the opportunity to study core academic subjects at GCSE and A-level, as well as raising their aspirations towards the most highly-selective university courses.
"We must also ensure that inspirational teachers in shortage subjects like physics, maths and foreign languages are encouraged to teach in schools serving less well off communities."