Two fifths of the people holding down Britain's top jobs went to a private school, according to a major report on the UK's unrelenting educational privilege.

As two Oxford graduates and former public school boys fight it out to be the next prime minister, the Sutton Trust published its annual round-up of the backgrounds of the country's professional elites.

The research group found 39% of some 5000 elite posts in the UK - including in industry - were held by people who went to an independent school - despite the fact thast only 7% of the population are privately educated. Thast means privately educated people are five times more likely to get a top job

That figure rose to 65% of senior judges, 59% of civil service permanent secretaries and 57% of the House of Lords. It was 39% for the current cabinet.

READ MORE: Only two Scottish Tory MPs privately educated as party claims it is open to all

The Sutton Trust also found that a quarter of top post holders had graduated from Oxbridge.

The group said its findings revealed a ‘pipeline’ from independent schools through Oxbridge and into senior jobs. An average of 17% across all top jobs came through this pathway, but this figure rises as high as 52% of senior judges, and one third of regular national newspaper columnists.

The frontrunner to be the next Tory leader, Boris Johnson, is a former newspaper columnist went to Eton and Oxford University. His rival, Jeremy Hunt, went to Charterhouse and then Oxford before going in to business and politics.

HeraldScotland: Mayor Boris Johnson

Boris Johnson

READ MORE: Revealed: MSPs five times more likely to be privately educated than average Scot

Sutton Trust figures are only for a UK elite. In scotland, slightly fewer people are privately educated. Herald analysis of MPs and MSPs north of the border has repeatedly shown lower levels of privilege in our politics.

The gap between Holyrood and Westminster, however, has narrowed. The proportion of privately educated MPs fell from 34 per cent in the 2010 intake to 32 per cent now.

Fully 20 per cent of politicians elected to Holyrood in 2016 went to independent schools, up from 17 per cent last in the last parliament. The change was largely because Conservatives replaced Labour as the biggest opposition to the SNP.

HeraldScotland: Jeremy Hunt: Attending Claygate clubhouse opening

Jeremy Hunt

Sport, the Sutton Trust found was the most democrative walk of life. Of 37 categories surveyed in the report, only among men and women footballers were the privately educated under-represented.

The Sutton Trust said Britain showed "isolated pockets of positive change, but a picture characterised by persistent inequality. The proportion of the elite who are privately educated appears to be decreasing, but change is happening slowly."

Grammar schools have declined in the elite dramatically, now numbering just 20%, half that of comprehensives (40%, up 9% in five years). This, The Sutton Trust said, reflected the move away from selective state education in the 1960s and 1970s.