Eton, its former head liked to point out, is a four-letter word. The elite school, whose pupils dress like old-style head waiters, is used to invective. But the hostility has new heft. The Labour party conference last month voted to integrate private schools into the state sector and redistribute their assets. The slogan of the campaign? Abolish Eton.

The mechanics would be worked out if and when Labour is in government. Outright expropriation is not on the agenda, it insists. But if there is compensation for an asset grab, how would it be calculated? Labour has suggested the cost of water nationalisation would be less than £15bn — the book value of the 15 English water companies. Lex has estimated that compensation for National Grid’s UK assets might be just £1bn more. A similar value looks plausible for the assets of independent schools.

One guide to their value is that it would cost nearly £19bn to replace them — £10.7bn for the land and £7.9bn in building costs — according to a study by Oxford Economics for the Independent Schools Council. But that used residential land prices. Without planning permission to change their use, existing private schools might not be worth so much.

Chart showing private school investments

Is there a more accurate way of doing this? The Girls’ Day School Trust, which has 25 schools teaching 19,000 girls around the UK, provides a sample. Its buildings and equipment are worth £392m. That implies a value of nearly £13bn for independent school assets, if scaled up to take account of all the UK’s 619,000-odd private school pupils. But property values are historic. Schools would hold out for more.

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Endowments and investments are also in the line of fire, to be redistributed across other educational institutions. If GDST’s investment funds of £123m are representative, those assets would total £4bn. In reality, endowments are very unevenly distributed. Those of the seven original ‘‘public schools” — Charterhouse, Eton, Harrow, Rugby, Shrewsbury, Westminster and Winchester — total £982m.

Chart showing the cost of replacing independent school

Such numbers do not represent anything like the true worth of the schools, famous for their brands and knowhow. But they might well be an overestimate of the compensation on offer. A Labour government might opt to ratchet up costs or tax endowments until independent schools had to switch to the state system to survive. Whatever the approach taken, the legal arguments will be epic. Schools, fighting for their lives, will defend themselves fiercely. “Abolish Eton” is a snappy slogan. Implementing it would be scrappy, costly and drawn-out.

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