Imagine that it’s 2020, Boris Johnson is gone, and you are the new British prime minister Jeremy Corbyn — or perhaps his more electable Labour successor. You are leading a coalition. Your mission is to make the UK fairer. British social mobility is “stagnant”, and a person’s background strongly predicts their future career, says the government’s Social Mobility Commission. The country’s elite passes down advantage from generation to generation: 64 per cent of Johnson’s cabinet went to private schools. All this unfairness helped prompt the vote for Brexit.

What reform would make Britain fairer? Nothing is off the table. Well, says a radical aide, why not abolish Oxford and Cambridge, just as French president Emmanuel Macron has promised to scrap his elite alma mater, the Ecole Nationale d’Administration? Oxbridge recruits more pupils from eight schools (six of which are thought to be fee-paying) than from 2,900 British state schools combined, and spits them out at the other end as the proto-ruling class. But most of your ministers blanch at destroying two ancient national assets. Finally, you agree a solution: keep what’s best about Oxbridge but stop it teaching undergrads. That removes Oxbridge’s biggest distortion of British life.

So far, the British debate about fairness has focused more on private schools than on Oxbridge. Public appetite for abolishing these schools faded after the 1960s, which is why even privately educated Corbyn isn’t proposing it. Still, Labour activists hope to put a motion before next month’s party conference that would commit Labour to “integrating” these schools into the state system. The plan (hashtag: #AbolishEton) would remove their charitable status and tax privileges, redistribute their assets and ensure universities “admit the same proportion of private-school students as in the wider population (currently 7 per cent)”.