Britain is a nation where the "small elites" educated at independent schools and Oxbridge are dramatically overrepresented across public life, according to the Social Mobility and Child Poverty Commission.

The government backed organisation, which monitors whether the UK is becoming a fairer place or not, examined the backgrounds of more than 4,000 business, political, media and public sector leaders.

The research revealed that more than seven in ten (71%) of senior judges, 62% of senior armed forces officers and more than half (53%) of senior diplomats attended fee-paying schools.

"This research shows that, despite decades of effort to open up opportunity in this country by successive governments, the UK's top jobs remain disproportionately held by people from a narrow range of backgrounds," said Alan Milburn, the chair of the commission and a Labour MP.

"The institutions that matter appear to be a cosy club. It is hard to avoid the conclusion that Britain is deeply elitist.

"In a democratic society, institutions – from the law to the media – derive their authority in part from how inclusive they are."

The study also found that cabinet members are five times as likely to have attended independent school as the population as a whole.

The research said shadow cabinet is three times as likely. Almost two in three Lords (61%) come from just 24 universities.

The report also said that large numbers of CEOs of the FTSE 350 (47%) and those in the Sunday Times Rich List (26%) were educated abroad.

Excluding these, 41% of British-educated FTSE350 CEOs and well over half of those in the Sunday Times Rich List (60%) were educated privately. Over a quarter of the Rich List (29%) did not attend University.

Milburn has called for a "national effort to break open Britain's elite".

He wants the government to lead by example in recruitment decisions by opening up top jobs in the public sector, collecting data on social background, tackling unpaid internships and addressing the funding gap for postgraduate degrees.