A privately educated elite continues to dominate the UK’s leading professions, taking top jobs in fields as diverse as the law, politics, medicine and journalism, according to new research.

The Sutton Trust educational charity has been carrying out similar surveys for more than a decade, and though it reports “small signs” of progress, this year’s results confirm what has long been known – that if you have a private education, you are considerably more likely to get to the top of British public life.

Although just 7% of the population attend independent fee-paying schools, the survey reveals that almost three quarters (71%) of top military officers were educated privately, with 12% having been taught in comprehensive schools.

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In the field of law, 74% of top judges working in the high court and appeals court were privately educated, while in journalism, more than half (51%) of leading print journalists went to independent schools, with one in five having attended comprehensive schools, which currently educate 88% of the population.

In medicine, meanwhile, Sutton Trust research says 61% of the country’s top doctors were educated at independent schools; nearly a quarter (22%) went to grammar school and the remainder to comprehensives.

In politics, the picture is a little better, with under a third (32%) of MPs having been privately educated, though that figure goes up to half of the cabinet, compared with 13% of the shadow cabinet.

Graduates of Oxford and Cambridge universities also continue to dominate the field, though they educate less than 1% of the population. In law, nearly three quarters (74%) of the top judiciary went to Oxbridge; 54% of the country’s leading journalists went to Oxbridge, and just under half (47%) of the cabinet attended Oxbridge, compared with 32% of the shadow cabinet.

Facebook Twitter Pinterest Award-winning British actors are more than twice as likely to have had a private education than award-winning pop stars. Adele, pictured. Photograph: Frank Micelotta/Rex/Shutterstock

The Sutton Trust’s Leading People 2016 report, which is published on Wednesday, tracks the educational backgrounds of leading figures in 10 areas of public life, among them film and music, which make an interesting contrast.

It reveals that award-winning British actors are more than twice as likely to have had a private education than award-winning pop stars. While 42% of British Bafta winners went to an independent school, just 19% of British winners at the Brit music awards were educated privately.

While Eddie Redmayne, star of The Danish Girl; Homeland actor Damian Lewis; and Tom Hiddleston, now starring in the BBC series The Night Manager, famously went to Eton College, the Sutton Trust points out that British music stars like Adele, Imogen Heap and Jessie J found success after attending the state-funded Brit School in Croydon.

The report welcomes a new focus on diversity and professional access, especially in the legal profession and the civil service, and says there are small signs that things may be “slowly changing in certain fields”.

In law, for example, while 76% of top judges attended private schools in the late 1980s, that went down to 75% by the mid-00s and is now at 74%. The report points out leading law firms have adopted a number of social-mobility programmes and the Solicitors Regulation Authority now collects data on solicitors’ educational backgrounds.

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In business too, partly because of the internationalisation of top posts, the report says the proportion of FTSE 100 chief executives educated at independent schools has fallen from 70% in the late 1980s to 54% in the late 2000s and 34% today.

And in journalism the tide may be starting to turn; in the mid-80s more than 90% of leading editors had attended either private or grammar schools. That figure has gone down to 80% today.

In politics, too, there are fewer privately educated members in the current cabinet (50%) than the 2010 coalition cabinet (which had 62%), but the proportion is still slightly higher than Tony Blair’s cabinet (44%) after the 2005 general election.

Sir Peter Lampl, chair of the Sutton Trust, said: “Our research shows that your chances of reaching the top in so many areas of British life are very much greater if you went to an independent school.

“As well as academic achievement, an independent education tends to develop essential skills such as confidence, articulacy and teamwork, which are vital to career success.

“The key to improving social mobility at the top is to open up independent schools to all pupils based on merit not money ... as well as support for highly able students in state schools.”

Russell Hobby, general secretary of school leaders’ union NAHT, called for better – and earlier – careers education in schools. “Once again the Sutton Trust has shown that not all professions are representative of the country at large, something school leaders will read with interest.

“Schools are engines of social mobility, showing that through hard work and application, all pupils can aspire to fulfil their potential, whatever that may be.”

Alan Milburn, chair of the social mobility commission, said: “This report underlines how those from less privileged families are too often shut out from Britain’s top jobs. But it also shows that where firms commit to fairness, progress is possible.

“From the civil service to the law, new schemes to widen access have been announced. But it is time to turn early promise into enduring commitment. Every profession and every large firm should have a clear strategy on social mobility and should publish data showing what impact their strategy is delivering.”

A Department for Education spokesperson defended the government’s record on social mobility and said thanks to its reforms 1.4 million more pupils are being taught in good or outstanding state schools than in 2010.

“University entrants are at an all-time high, with rising numbers of children from disadvantaged backgrounds going to university and the number of disadvantaged students attending Russell Group universities doubling since 2010.

“We are determined to spread this educational excellence everywhere, extending true social mobility for all. We are continuing the pupil premium at current rates for the duration of this parliament, providing billions of pounds to support disadvantaged pupils reach their potential.”