Private education is just one way the privileged are given their advantages. It starts from birth. Affluent parents have babies with higher birth weights. They have less cramped houses, meaning better well-being and more quiet places to study.

Better-off parents tend to have more formal education and more "cultural capital". A big gap in vocabulary between richer and poorer children opens up when they're very young. Their parents can afford private tutoring. Diets are better and their children never go hungry

Poverty can impose specific stresses on family life that the affluent tend not to have. Poorer children are more likely to suffer from mental distress and poorer physical health, all of which impact educational attainment.

Private schools do better not because their teaching is superior, but mostly because pupils have multiple advantages given to them by the family they're born in.

That doesn't mean they don't get advantages, like networks, confidence, sophisticated Oxbridge prepping.

Segregating children by the bank balances of their parents cements and reinforces inequalities. But we need a much broader conversation than private education: we need an all out war on the inequalities that hold back the huge potential of so many less advantaged children.

That algorithm which benefited the privately educated and downgraded pupils from poorer backgrounds is a grotesque metaphor for a society systematically rigged in favour of the privileged and against those lacking advantages from the very day they are all born.