As teenagers find out their exam results after what’s been a particularly stressful A-level year, I can’t help but think of how different the experience may be depending on whether your parent is, say, a cleaner or a barrister.

Ministers have been accused of a “total and abject failure” to widen access to top universities for disadvantaged students, after analysis by the Labour party found the proportion attending Russell Group universities had increased by only one percentage point since 2010. At the same time, educational charities warned this week that middle-class pupils and their parents were increasingly using university clearing to shop around for the best courses, to the detriment of their less well-off peers. This is the same old story; as with every other advantage wealth in education creates, those with affluent parents and schools can play the clearing system ahead of their poorer peers.

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Working-class families are repeatedly told that if they apply their talents they will buck this trend, as if enough effort can counter entrenched structural inequality. But Sutton Trust research this month shows that even disadvantaged pupils who perform well at primary school are less likely to get top grades at secondary school than their wealthier peers. That’s without considering the impact of disadvantage on pupils who find learning harder; children who are having their teaching assistants cut, while their parents – hit by low wages, squeezed benefits and high rents – are increasingly up against it to provide their children with even a quiet bedroom and regular meals.

From a child’s early home life, through exams, to university admission, social and economic inequality is ever present. What’s the grand plan to deal with this? Last week, education minister Nadhim Zahawi suggested his own priority: a government-backed scheme under which 40 private schools provide boarding places for looked-after children. Referencing Jeremy Corbyn’s 2017 manifesto proposal to abolish the VAT exemption on school fees, Zahawi told Newsnight that Labour “would never be able to abolish” private schools if they helped to improve the life chances of vulnerable children.

Advocating using children in care as human shields to protect private school funding is a particularly grubby move, but does point to how unreasonable this debate is. In a climate in which the state sector is so starved of resources that the Guardian reported this week that some headteachers now spend more than half their time fundraising for essential subjects, charity status has increasingly become contentious. Even Theresa May pledged in the Conservative 2017 manifesto to force independent schools to sponsor a state school or risk losing their tax breaks (she later quietly dropped it). These are not insignificant sums. Between 2017-22, private schools will get tax rebates totalling £522m as a result of their status as charities.

The Charities Act defines a charity as an institution that’s established for a charitable purpose and “provides benefit to the public”. While the remit of the “advancement of education” means private schools fall into this category, you would be forgiven for balking at it. Rather than providing “benefit to the public”, modern private schools too often actively harm it, giving a tiny minority of already advantaged offspring a further leg up at the expense of already disadvantaged children.

Facebook Twitter Pinterest ‘Education minister Nadhim Zahawi MP said Labour “would never be able to abolish” private schools if they helped to improve the life chances of vulnerable children.’ Photograph: David M. Benett/Getty Images for Bell Pottinger

Schools such as Winchester, Eton, St Paul’s and Westminster all started out as philanthropic institutions but have long since turned into mechanisms for a form of social apartheid, where the natural human instinct to give our child the best is used to justify the wealthiest 7% gaining a stranglehold on Britain’s legal, media, political and business institutions. As Robert Verkaik writes in his blistering book, Posh Boys: How the English Public Schools Ruin Britain, “The public schools were founded to educate the poor and ended up serving the interests of the rich.”

As Verkaik argues, the golden rule for charitable status should logically be how many children are educated without their parents having to find a fee, but, in 2017, incredibly, only 1% of private school pupils were schooled for free. Worse still, “financial assistance”, which proponents of the private education sector frequently point to, is largely going to wealthy families. In June, it emerged that private schools are spending millions more on giving affluent middle-class families fee discounts than on children from disadvantaged backgrounds, including discounts for staff, siblings and offspring of senior armed forces personnel and members of the clergy. Even the means-tested bursaries include help for families on incomes as high as £140,000. (It’s worth noting that many high-earning military families already benefit from government subsidies that pay fees at elite schools including Eton.)

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This is reminiscent of the argument that private schools help comprehensives by taking some burden off the state, when all the evidence suggests that siphoning off affluent pupils – and the power of their parents – damages the state education system. Besides, even if private schools did genuinely earn their tax break by charitable bursaries, this is in itself regressive; elevating a few talented low-income pupils through social mobility, while sweetening the entrenchment of the status quo.

Few would claim that the charitable status given to private schools is the greatest challenge facing Britain’s education system – nor that removing it would go anywhere near far enough to level the playing field between children from low-income and wealthy families, or address the wider dominance of private schools. But giving these schools a tax break is a manifestation of how warped our system of equal opportunity is – one that not only allows some to buy better life chances than everyone else, but gives them a tax break for the privilege.

If Britain genuinely wants to be a society where talent, rather than money, matters, all of us – including ministers – need to have a real conversation about what that entails. Private schools’ charitable status is surely a good place to start.

• Frances Ryan is a Guardian columnist