The heads of Britain’s private schools are really feeling the pressure. How else do you explain their desperate plea to be left alone because super-rich parents are saving the taxpayer billions of pounds a year by sending their offspring to Eton and Harrow? This self-serving study in public school economics published by the Independent Schools Council (ISC) was given pride of place in at least two national newspapers last week. It’s an old argument that was first shot down in 1968 by a panel of academics and private school leaders set up to “integrate the public schools with the state system”. The Public Schools Commission found the claim that parents who chose to pay for their child’s education were being hit with a double taxation “unimpressive”, likening it to a childless couple asking for a tax rebate because they weren’t drawing any benefit from the schools system.

Similarly, the Charity Commission in 2009 considered the same contention to be specious when it was challenged by private headteachers over plans to make their schools perform their charitable function. A more modern analogy might be a Russian oligarch boasting that, by using his helicopter to get to work, he is saving the British taxpayer thousands in road maintenance.

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But in its latest report, the ISC has gone even further by claiming that the “induced impact” of its schools boosts the country’s GDP by a massive £13.7bn. This figure includes the employment of armies of teachers, grounds staff, caretakers and catering staff, together with all their personal expenditure. The misplaced assumption seems to be that, should the private schools pass into state ownership, they would stop making a contribution to the national coffers. Of course they wouldn’t.

This is desperate stuff. But perhaps the schools feel they have their backs to the wall. Heaving into view is the very real prospect of a Jeremy Corbyn government and a pledge to impose VAT on private school fees – a tax that would make a genuine £1.5bn contribution to the national coffers. Even the Tories, once loyal friends of independent schools, have vowed to remove charitable status from those that continue to do nothing charitable.

I’ve been told that next month a newly formed parliamentary group will call for the phasing-out of our private schools. The group wants to replicate what Finland managed in the 1970s when all-party support was gained for creating a national education system – under which its children continue to dominate the OECD education outcome tables.

If the cold winds of change are blowing in the direction of the independent school sector, then its headteachers only have themselves to blame. The writing was on the wall as long ago as 1940; when Winston Churchill called on the president of the Board of Education to fill public schools with “bursary boys”. Since then the sector has had countless opportunities to reconnect with local communities. Instead, today just 6,000 (one in 100) privately educated pupils are on 100% bursaries.

When Eton College and Winchester College were first established 600 years ago, it was written into their charters that all pupils would be poor scholars taken from the community. But the schools were hijacked by the wealthy, who used them to educate their own children, and in so doing their charitable purpose was corrupted to accentuate the advantage of already privileged children.

Through vested interest and undue influence, the schools have staved off meaningful reform since Churchill’s call. So we now find ourselves in the ludicrous situation where a charity such as Eton, which educated Prince William and David Cameron, is able to claim millions of pounds of tax savings each year, while asserting that it is doing us all a favour by not troubling the state sector with the education of future kings and prime ministers.

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In recent times this country has undergone a private school population explosion, with the number of pupils doubling from 300,000 in the 1970s to more than 600,000 today. More children than ever now benefit from an apartheid system that allows 7% of the population to buy advantages over the rest of society.

It is an advantage that has been sharpened to the point that a child at a secondary private school has three times more money spent on his or her education than one at a state school. The ISC’s own data shows that in the past 10 years, average annual school fees have increased by up to 50% to £33,000 for boarders and £15,000 for day pupils. Compare this to around £6,000 currently spent by the state on each pupil, a figure that has grown by a much smaller percentage over the same period.

With so much more cash pouring into the private sector, it is hardly surprising that its pupils are over-represented at Oxbridge (40%), in the senior judiciary (74%) and in the House of Commons (32%). So is it any wonder, as we look on with horror at the democratic crisis created by the current crop of politicians, that we question the educational backgrounds of our leaders? Theresa May, Jeremy Corbyn, Nigel Farage, Boris Johnson, Jacob Rees-Mogg, even Caroline Lucas, all benefited from a private education advantage. The time is right to urgently examine a system that gives so much to a select few but denies millions of children a fair start in life.

•Robert Verkaik is the author of Posh Boys, How the English Public Schools Ruin Britain