Theresa May’s desire to return England to grammar schools is her first real spasm of Trumpism. It is incoherent. It makes no sense educationally, financially or politically. It is also based on a lie, that selection is about parental choice. May seems unaware that parents do not choose grammar schools, grammar schools choose children.

The policy was alluded to in the budget by the chancellor, Philip Hammond, though he only mentioned more money for free schools. Budgets have a poor record in education reform. Last year, George Osborne declared every school in England was to become an academy. By summer the policy was in disarray, and by October it was dead.

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The education budget is so stretched it must cut capitation payments to schools by 8% over the next three years. A new central “funding formula” is also slashing grants to individual schools by as much as £400,000. Yet Hammond can reportedly find £320m for 110 new free schools, which could be “selective”.

Reviving 11-plus selection for grammar schools has been dismissed as “disastrous” by the outgoing inspector of schools, Sir Michael Wilshaw. It is opposed by the Tory-chaired Commons education committee, and even, reportedly, by the education secretary, Justine Greening. Last November, all 64 secondary headteachers in the Tory education authority of Surrey declared their “deeply held vehement opposition” to the change. Even the elite scientists of the Royal Society concluded from an Education Policy Institute study of existing selective schools that there was no evidence grammars raised standards of science schooling overall. There was certainly none to indicate “that overall educational standards for free school meals pupils … would be improved by an increase in the number of places in selective schools”.

May should remember history. Selection for grammar schools under the 1944 Education Act was based on the theory, associated with the psychologist Cyril Burt, that inherited or innate intelligence could be measured at 11, and children pigeonholed into separate schools accordingly. The theory was cruel and later discredited. But it was seized on by those who wished to institutionalise the prewar social divide between grammar schools and elementary schools, then reborn as “secondary moderns”. Champions of selection boldly declared, however, that every child would have “equal opportunity”. There would be “equality of esteem” between types of school, a stress on social mobility and tutor-proof testing.

A non-academic “intelligence test” would render selection blind to attainment or previous teaching. It would be ruthlessly fair.

This selective system became so widely hated it had to go. Not least of its enemies were Tory parents appalled to find their children declared “failures” and sent to a secondary modern with “rough boys”. After Labour’s 1964 election victory, with a pledge to end selection, the Tory education spokesman, Sir Edward Boyle, was told at party meetings to abandon the 11-plus. That was why Margaret Thatcher, as education secretary in 1970, knew better than to halt comprehensive reorganisation.

There is an intriguing difference between then and now. May says she wants selection on the basis of “academic ability”, which is as sure a social selector as you could ask. It is why the 11-plus, in the 15 areas where it survives, has morphed from an intelligence test to an attainment exam. In places such as Kent, Trafford and Buckinghamshire, better-off parents tutor their children fit to bust, and if they fail, struggle to go private. There is no way to make these admissions “tutor-proof”. At least the old 11-plus made a stab at social equality.

Leaks have suggested that May wants 10% of each cohort to be selected. This will skim the brightest pupils, and teachers, from the majority of local secondary schools, and cannot fail to do them harm. If, again as trailed, selection is biased towards social disadvantage, access will be even narrower. May’s policy will have excluded Tory parents howling for her blood.

As Hammond implied, free schools can already become grammars, with some 500 in place or planned, and free to choose pupils at will. Carried to its conclusion, this is a highly divisive school system. It is also costly. Free schools have already proved extravagant foibles, costing 60% more per pupil than council schools. The public accounts committee has calculated that £240m had been blown on 40 free schools that were simply not needed.

May’s grammar schools will be free schools with a heavy bureaucratic overlay of state control, to ensure only the brightest get in. Whatever she says, she knows this tired search for “a public sector Eton” will merely increase social segregation, communal division, “white flight” and add to stress and misery among children at their most vulnerable age. It will do nothing to help the bulk of children, richer or poorer, for whom Britain’s overwhelmingly comprehensive secondary schools give a perfectly sound education.

Ever since school planning and budgeting were removed from local authorities in the 1990s, state schools have, like hospitals, been subject to constant upheaval and expense. Ministers frantic for headlines are ever more obsessed with exams, targets and league tables – witness their fixation with maths results to compare with Singapore and China.

Such is the opposition to a revival of selection that local councils will probably refuse to have all their 11-year-olds sit an exam for a handful of places at May’s glamour establishments. They will be left with yet another vagrant institution to add to the academies, specialist schools, free schools and technology colleges, relics of some passing minister’s whim for novelty. Money will be wasted. Headteachers will resign in despair. The victims of these battles, the children, will soldier valiantly on.

This is all a distraction. Its educational corpse-worship is apparently the idea of May’s chief of staff, Nick Timothy, unsurprisingly a former lobbyist for free schools. Domestic policy is reduced to a bauble to flatter the vanity of a Downing Street courtier, a Trump moment indeed.