“The only natural resource this country will have in 20 years is the intelligence of its young,” Dr Stephen said. “But we don’t have a fast lane in the UK. Of the people who tried to murder me when I worked in remand homes, two were amongst the cleverest people I have ever met. You ask any teacher who they are most frightened of in terms of discipline: it’s the clever ones. If you neglect intelligence it goes septic, it turns sour.”

So the experiment in channelling Britain’s wasted raw intelligence starts here. Educating a son at St Paul’s School now comes at a high price, but it was founded in 1509 by John Colet, Dean of St Paul’s Cathedral, to be free to any bright enough to make it in. This is Dr Stephen’s dream: to become as progressive as they were 500 years ago. He has committed St Paul’s to going “needs-blind”, admitting pupils exclusively on merit and then charging according to their parents’ ability to pay. He believes that this could spread beyond this leafy patch of West London to the entire private education system.

“What we are primarily doing is deciding to turn the clock back to 1509,” he said. “If you’ve got your own endowment you’re truly independent. You look at that founding statement in 1509: to educate boys from ‘all countres and naciouns indifferently’. It’s an extraordinary statement. A school like this should be a college of all the talents. It’s as simple as that. And we would like to admit anybody regardless of race, colour, creed or social and economic background.

“This is an idea whose time has come. Actually, it is an idea whose time has never gone, but it simply went into recession for a short period.”

The school’s governing body has voted to back the move and the target date for going completely “needs blind” is 25 years from now. The first step is to raise the number of pupils on bursaries, which usually pay about 80 per cent of fees, to a fifth of the intake as soon as possible.

Partly a privatisation of the grammar school ideal, partly a way of making public schools truly public, this kind of transformation is uncharted territory. So, although Dr Stephen is enthused, much of the plan raises more questions than he can at this point answer. You get the feeling that the teacher, like the brightest pupils, is winging it a little.

Take the cost: it is astronomical. Each “free” child needs an endowment of between 20 and 25 times the school’s annual fees of £15,000 because Dr Stephen is adamant that they are not to be subsidised by paying parents. To offer free education to all who might be eligible would, Dr Stephen said, eventually require an endowment fund of at least a couple of hundred million pounds. The only independent school in the country that is “needs-blind” is Christ’s Hospital, near Horsham, West Sussex, with an endowment of around £350 million. Contrary to popular belief, St Paul’s has little money in the pot and faces a near-total rebuilding programme. And, although he takes “unashamedly” as his model the huge endowments of Yale and Harvard universities that allow them to fund thousands of students, Dr Stephen has not a single dedicated fundraiser. Almost as big is the problem of selection.

“There is a popular myth that the minute a school like this offers free places, the entrance exam day will look like the auditions for the new performance of Oliver! — thousands of barefooted children queueing up at the door. It’s just not like that.” By contrast with the North, where he lived during his ten years as head of the private Manchester Grammar School, the South East, he says, has no tradition of poorer children taking a shot at independent schools. “There is no culture in London that says, I don’t have a lot of cash but I have a reasonable aspiration to send my son to St Paul’s. What you have to do first of all is change that culture, or rather create that culture.”

Other schools are already in talks about becoming more “needs blind”; it is pushing at an open door, Dr Stephen says. Meanwhile he is preparing to set up, with head teachers from about ten London private schools, a consortium with a central bursaries hotline for families daunted by the process.

“You need to make the point of contact very easy,” he said. “It cannot be intimidating. In the end it goes down to simple things like the first voice on the end of the phone, because you must assume that the people ringing in do not have prior experience of plotting their way through the minefield of independent education in London, for which you virtually need a degree as a parent.

“We are actually saying X school offers X bursaries, this is what you have to do, these are the hoops you have to jump through, and it is also an attempt to offer a host for the first meeting. Walking up the drive of an independent school can be an extraordinarily daunting experience for those not used to it. The key thing is information without patronisation.” But once in the door, how to compete with wealthier parents who go to obsessional and expensive lengths to drill their offspring for demanding entrance exams? He is convinced that the 20-minute interview they now use is able to weed out a hothouse flower from a truly gifted ten-year-old. Among the things they look for (private exam tutors take note) is a sense of irony and passion.

“It is not the answers that matter so much as simply to see the cogs turning,” he said. “Actually a child who is coached for that interview tends to perform very poorly. It is almost impossible to coach someone in the use of irony. You can give them an ironical example, but to actually use irony is really an advanced technique, which is actually much better linked to raw IQ. I worked in remand homes for a year, by and large with people with no academic qualifications whatsoever. I have never known a more brilliant use of irony than the inmates in the remand home.

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