As a result, private school pupils who score the equivalent of two B grades and an A at A-level are almost 10% more likely to get a place on one of the 500 most selective degree courses (79% against 70%) according to a study by the Sutton Trust, and the Department for Business, Innovation and Skills.

It also found that teenagers educated privately were three times more likely to apply to leading universities - including edinburgh and St Andrews - than those at further education colleges.

The Trust, which aims to improve educational opportunities for young people from underprivileged backgrounds, warned that state schools are not providing bright pupils with the guidance they need to combat a perception that leading universities are "not for for the likes of us".

The University and College Union (UCU) claimed the study showed that Britain is suffering from a "poverty of ambition".

The study analysed information on hundreds of thousands of students using information from the university applications service Ucas, and the National Pupil Database.

It found that teenagers from the top fifth of private schools made on average 2.11 applications to the "Sutton 13" universities. Pupils from the top fifth of comprehensives made 1.03 applications and those from FE colleges made 0.8 applications.

Trust chairman Sir Peter Lampl said: "This research shows that even with the right grades in the right A-level subjects, thousands of state school students each year do not apply to the most academically selective degree courses.

"Many highly able pupils from non-privileged backgrounds wrongly perceive the most prestigious universities as 'not for the likes of us', and often lack the support and guidance to overcome this misconception."

He said the research provides another reason for reforming the university application system.

"Students should be able to apply to higher education on the basis of their actual results rather than predicted grades, which can be inaccurate.

"This simple step towards post qualification applications would give many non-privileged students the confidence to aim that little bit higher," he said.

UCU general secretary Sally Hunt said: "It is deeply concerning that in 21st century Britain where you live still plays such a big role in where you are likely to study. This poverty of ambition is holding Britain back and is very damaging in these tough economic times."

Wes Streeting, president of the National Union of Students said: "We welcome the Sutton Trust's recommendation that the university application system should be reformed. Post-qualification applications would enable someone's actual achievements to be taken into account, rather than one teacher's predications."

Business Secretary Lord Mandelson said: "Hard work and talent should create success, whatever a person's background. There are more students in higher education than ever before, with the proportion of people from poorer families going to university having grown by 3% since 2002."

Last month, in his first speech on universities, Lord Mandelson said more needed to be done to widen access to university.

He said: "We are doing better, but not well enough. I am impatient about this progress and intend to turn up the spotlight on university admissions."

The "Sutton 13" universities are Birmingham, Bristol, Cambridge, Durham, Edinburgh, Imperial College, London School of Economics, Nottingham, Oxford, St Andrews, University College London, Warwick and York.