Britain is still "deeply elitist" with privately-educated pupils and Oxbridge graduates continuing to dominate top roles in society, a major new report warns.

Many of the nation's judges, politicians, armed forces chiefs, journalists, TV executives, public officials and sports stars attended fee-paying schools before going to to study at Oxford and Cambridge, it suggests.

This stark lack of diversity means that many of Britain's key institutions are not representative of the public they serve, and the people running them may not understand the daily issues facing people from different backgrounds, according to the Social Mobility and Child Poverty Commission.

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The commission's chair, Alan Milburn, said the findings were a wake-up call, and suggested that institutions need to open their doors to a broader range of talent.

The study analysed the backgrounds of more than 4,000 individuals holding top jobs in British society.

It concludes that Britain's elite is still "formed on the playing fields of independent schools" and "finished in Oxbridge's dreaming spires".

More than seven in ten (71%) of senior judges, 62% of senior armed forces officers, over half of permanent secretaries (55%) - the most senior civil servants in government - 53% of senior diplomats, 45% of public body chairs, 44% of the Sunday Times Rich List, 43% of newspaper columnists, 35% of national rugby teams, a third (33%) of the England cricket team and 26% of BBC executives attended a fee-paying school, the study found.

Former private school pupils are also over-represented in politics, with half of the House of Lords attending an independent school along with over a third (36%) of the Cabinet, a third (33%) of MPs, and 22% of the shadow cabinet.

Nationally, around 7% of the UK population attended a private school, the study says.

The statistics also reveal the numbers in each profession who went to Oxford or Cambridge.

The most over-represented professions were the judiciary, with 75% of senior judges attending one of these two universities, along with 59% of the Cabinet, 57% of permanent secretaries, and 50% of diplomats.

In addition, 47% of newspaper columnists are Oxbridge graduates, as are 38% of the House of Lords, 33% of the Shadow Cabinet and 24% of MPs.

The study compares this with the adult population, which shows that 62% of UK adults have not been to university, one in nine went to Russell Group universities and less than one in 100 graduated from Oxford or Cambridge.

"Our examination of who gets the top jobs in Britain today found elitism so stark that it could be called 'social engineering'," it says.

The study suggests that a lack of diversity in the people running the nation's top institutions is worrying because it risks a lack of understanding with those from different backgrounds, and because it puts limits on social mobility - meaning that the prospect of making it to the top of a profession is limited for someone who does not have a certain school and university background.

It adds that the "sheer scale of the dominance of certain backgrounds" raises questions about whether getting a top job is about ability or knowing the right people.

Mr Milburn said: "This research highlights a dramatic over-representation of those educated at independent schools and Oxbridge across the institutions that have such a profound influence on what happens in our country. It suggests that Britain is deeply elitist."

He added: "Locking out a diversity of talents and experiences makes Britain's leading institutions less informed, less representative and, ultimately, less credible than they should be.

"Where institutions rely on too narrow a range of people from too narrow a range of backgrounds with too narrow a range of experiences they risk behaving in ways and focussing on issues that are of salience only to a minority but not the majority in society.

"Our research shows it is entirely possible for politicians to rely on advisors to advise, civil servants to devise policy solutions and journalists to report on their actions having all studied the same courses at the same universities, having read the same books, heard the same lectures and even being taught by the same tutors.

"This risks narrowing the conduct of public life to a small few, who are very familiar with each other but far less familiar with the day-to-day challenges facing ordinary people in the country."

Mr Milburn said there is a risk that the more that just a few dominate key roles in society, the less likely it is that others think they can take part, leading to a "closed shop at the top".

The study says the data suggests that the "grip" of the narrow social group that are currently in the top jobs will only loosen slowly in the future and calls for a national effort involving government, parents, schools, universities and employers to "break open" Britain's elite.

Lee Elliot Major, director of policy and development at the Sutton Trust, said: "These stark findings build on Sutton Trust studies to show that Britain's top professions remain the preserve of the privileged few. We welcome the commission's recommendations, many of which we are addressing through our programmes that focus on increasing access to top universities and professions including law, banking and medicine.

"Whilst we are making progress with the young people we work with, it's clear that more needs to be done at Government level to address the issue of low social mobility."

Tessa Stone, chief executive of educational charity Brightside, said: "'The new report from the SMCPC lays bare an issue that we at Brightside tackle every day: that too many people in the UK are held back from top jobs because of their background, not any lack of talent.

"Our mentoring provides young people with inspiring role models who can help them into universities and careers they might otherwise have only dreamt of."

Shadow education secretary Tristram Hunt said: " Government policy is at odds with the commission's prescriptions. Alan Milburn, rightly, is very clear on the role for schools in ensuring children from deprived backgrounds get the exam results and broader character skills that they need to succeed.

"That vision is at the heart of Labour's schools policy. By contrast, Cameron's schools policy has done away with work experience and face-to-face careers advice - so important for young people - whilst ignoring the important role of children's character development in schools."