Robert Verkaik could hardly have picked a better time to publish this. One notorious posh boy (Eton, Oxford) exits Her Majesty’s Foreign and Commonwealth Office, another (Charterhouse, Oxford) arrives to take over. No surprise there, but the nation, or the 93% of it that did not go to private school, is left wondering again how this crony class of bought privilege and vicious self-interest has managed to hold on to the reins for so long. Not least when – from Balaclava to Brexit – they haven’t run things very well.

Of course, it may be that the grockles and plebs are not very bothered. In his fascinating, enraging polemic, Verkaik touches on one of the strangest aspects of the elite schools and their product’s domination of public life for two and a half centuries: the acquiescence of everyone else. “Public schools have a mesmerising influence over British people,” Verkaik says, echoing George Orwell (Eton) 85 years ago. Verkaik says we are all seduced, not least by the innocent question: “Who doesn’t want the best for their children?” As a parent and a troubled posh boy myself, I understand him.

It’s a leap from that thought, however, to educating your children privately – especially since the cost of an independent day school is more than £250,000 from nursery to sixth form. But the habit is not going away: school rolls have been stable since 2000, around the time Harry Potter turned up at Hogwarts. That is first because the investment is likely to work, in terms of buying access to university and life’s material prizes. More important is that as faith in the state system fails, the better the private one will fare: the one “hangs like a shadow” over the other, an expert in international education policy tells Verkaik.

Sending the children off to private school has long been the most notable hypocrisy of the leftish middle class, and of some of the public schools’ most famous detractors. Nadine Dorries (Halewood Grange Comprehensive), the rightwing Conservative MP whose outburst against “arrogant posh boys” David Cameron (Eton, Oxford) and George Osborne (St Paul’s, Oxford), gives this book its title, sent both her daughters to Ampleforth, where they have learnt “very good manners”. Paul Weller, whose wry bitterness as a member of the excluded class wrote the Jam’s song Eton Rifles, sent his children to public school. Eton might well have taken the little Wellers, I imagine, for about £35,000 a year: among the wiser self-preservation systems of the schools is the fact that they will allow some entry from outside the establishment. Otherwise we would have smashed them to the ground decades ago, wouldn’t we?

Verkaik’s larger theme is the toxification of British public life by the private school system and the injustice and inequality that educational apartheid based on wealth entails. But the blatant theft of public resources is the book’s sharpest point. From the very beginning the institutions – including St Paul’s, Winchester and Eton – have been hijacked by the wealthy, though they were plainly set up to benefit the poor.

Edinburgh’s Fettes college, a 19th-century invention, was built on the money of a merchant, Sir William Fettes, who left his fortune specifically for the education of the city. His executors instead constructed a gothic horror that sits behind high fences, with its great spire thrusting a finger up at the rest of the city. It has a poor record when it comes to sharing facilities or giving means-tested bursaries. Yet, like most, it is a charity: it pays a fraction of ordinary business rates and no VAT. Fettes receives an estimated £1m a year in direct subsidy from the Ministry of Defence, which still pays for much of the education of armed forces officers’ children. Tony Blair is one Fettes alumnus: Verkaik thinks it significant that his administration backed off from years of Labour pledges to sort out the absurd tax advantages the private school business enjoys.

How do we sort this out? Even a Jeremy Corbyn administration will be wary of the best-connected lobby groups in Britain (and of course Corbyn, shadow chancellor John McDonnell and Momentum founder Jon Lansman all did time at various Hogwarts). Besides, with 30% of students from abroad, the public schools are now a significant export industry. In Scotland the SNP, however, has promised to act on the exemption from business rates.

Verkaik’s solution is “slow and peaceful euthanasia”. He would suffocate the schools. Since they cater to just 7% of the population, let quotas be set, so that from their ranks come just 7% of judges (instead of 74%), 7% of senior forces officers (instead of 71%) and so on. Newspapers such as this (the British media is 50% private school-educated) will have to take the same medicine.

My money says private schools will survive: since the second world war successive governments have failed to curtail them in any significant way. As it happens, the departure of Boris Johnson means a Conservative cabinet without a son of Eton for the first time since the 1830s. But that won’t go on long – there are 20 Old Etonian MPs, all Tories. As an Eton school song has it: “Floreat Etona, Floreat, Florebit”. May Eton flourish; she will flourish.

Alex Renton’s Stiff Upper Lip: Secrets, Crimes and the Schooling of a Ruling Class is out in paperback (Weidenfeld & Nicolson, £9.99)

• Posh Boys by Robert Verkaik is published by Oneworld (£16.99). To order a copy for £14.44 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99