Are you posh enough to get a top job? That is the question being posed by Alan Milburn – a man often referred to, ironically, as the government’s social mobility “tsar”.

His Social Mobility and Child Poverty Commission has published a report on how class, accent and background are apparently preventing working-class people from entering some professions.

While only about seven per cent of children in England go to independent schools, trainees at some top law firms are more than five times more likely to have attended a private school than the average person.

The report draws on interviews with senior managers to discuss some of the reasons why working-class people are being shut out of top jobs – or failing to apply in the first place – but most of the evidence is anecdotal.

What do the statistics tell us about the continuing influence of the privately educated on the upper echelons British society?

Etonians sit on the wall and react as the Collegers and the Oppidans teams compete during the Eton Wall Game at Eton college in Eton

How much does a private education cost?

This report by the Centre for Economics and Business Research (CEBR) sets out the average cost of a private education in 2014: £12,400 a year for day fees and £28,800 for boarders.

Extras like uniforms, music lessons and school trips typically add £3,000 a year to the bill for a child at a day school.

The CEBR analysis shows that the cost has risen way above inflation in recent decades:

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Are private schools value for money?

Last year the Institute for Fiscal Studies found that the privately-educated tend to earn more than people who go to state schools – as much as £4,500 a year, on average, three and a half years after graduating.

But this could be explained by the fact that private school alumni are more likely to go to the best universities and tend to be over-represented in the highe-earning professions.

Even when the researchers filtered for these things, they found there was still a “premium” attached to a private education.

These average differences increase over the following three years, such that those who attended private schools (who report earnings 3.5 years after graduation) earn around £4,500 more per year, on average, than those who attended state schools.

In other words, if you took two people with the same degree from the same university who were doing the same job – but only one went to an independent school – that person still be likely to earn more.

How much? £1,500 a year. Pretty good. But compare that to the cost of attending the average day school for the full seven years – around £108,000 including extras.

You would have to earn that private school premium every year for 72 years to cover the cost of your education.

Is there a cost to the taxpayer?

The Independent Schools Council, which represents most private schools, says 80 per cent of its members have charitable status, which comes with tax benefits.

It’s not clear how much money independent schools save by declaring themselves charities. The Labour MP Simon Danczuk released figures from the Valuation Office Agency suggesting the sector would have to pay an extra £136m if they were stripped of business rate relief.

But other analysis suggests private schools add significant amounts to the economy.

A report for the Independent Schools Council by Oxford Economics claimed private schools add about £11.7bn a year to GDP and pay £4.7bn in tax revenues.

And they save the taxpayer a further £3.9bn a year by educating children who would otherwise have to be paid for by the state.

The paper also says private schools add about £1.3bn a year to GDP because they generate better educational performance.

But this implies that if we scrapped private education tomorrow, all that attainment would simply disappear.

It may seem far-fetched, but Finland made it illegal for schools to charge fees in the 1970s, without noticing a dip in educational achievement.

In fact, the Nordic country regularly features at the top of the OECD’s international school performance tables, although it is unclear how much this has to do with the decision to scrap private education.

Do privately-educated pupils perform better?

Yes and no. Privately educated pupils as a group are more likely to get better A levels, go to a good university and get a good degree.

But it is debatable how much of that is down to the school. Independent school pupils tend to be wealthier and to come from a higher social class, which makes them more likely to succeed irrespective of the school.

Studies that have tried to allow for family status and background have found little advantage in private education.

This OECD analysis concluded that state schools with similar student populations offered “the same advantages” as private schools in most of the countries they looked at.

Last year the Higher Education Funding Council for England found that private school pupils tended to go into university with higher A-level grades and come out with better degrees.

But if you compared students with the same academic performance, the state group did better:

“Students who have remained in the state school sector for the whole of their secondary school education tend to do better in their degree studies than those with the same prior educational attainment who attended an independent school for all or part of their secondary education.”

Do privately-educated people really still run the country?

Some 32 per cent of MPs in the new parliament went to a private school, slightly down from 35 per cent in 2010.

Half the cabinet went to fee-paying schools, compared to 62 per cent in the previous cabinet.

Mr Milburn’s commission went through many professions last year and found that the privately-educated are disproportionately represented in many walks of life, from the judiciary to worlds of sport, music, and the media.