It was an Oxford mathematics lecturer who under the pseudonym Lewis Carroll wrote Alice Through the Looking Glass. I rather felt as if I were in that mirror world of paradox when I rang up Professor Anthony Grayling, who has just unveiled a new private sector college offering what it claims to be "Oxbridge" level facilities to students whose parents are prepared to stump up £18,000 a year in fees – cash upfront.

Grayling, who describes himself and the other professors he has lined up to be lecturers (such as Richard Dawkins, Peter Singer, Linda Colley and David Cannadine) as "pinkos", is trying, it seems, to come to the rescue of those whose expensive private education has not gained them the intended places at Oxford or Cambridge. That, at least, is the impression of the Tory London Mayor Boris Johnson, who wrote yesterday of being assailed by wails from Oxbridge-educated parents of public schoolboys whose allegedly stellar A level and GCSE results had not gained them a place at dad's alma mater, and who were convinced that "there was some kind of secret Pol Pot-style persecution of the children of the bourgeoisie". The mayor went on to say that he had as a result thought of founding what he called "Reject's College, Oxbridge" – but now Professor Grayling had beaten him to it.

When I rang Grayling yesterday, I had expected him to shrink in horror from the idea that this was anything like the truth about his "New College of the Humanities"; but this is the mirror world, and so instead the self-described leftie volunteered how he had been influenced by a teacher at £33,350 a year Winchester College who had told him how many of his "brilliant" students had failed to get into Oxford or Cambridge, and how he, Grayling, would be thrilled to offer them places; indeed, he accepted the view of that Winchester teacher that "social engineering" – that is, the Government's pressure on Oxbridge to take more state-educated pupils with less stellar exam results – was at work here.

Anyway, one man I thought would warmly embrace Grayling's innovation was Dr Terence Kealey, the Vice-Chancellor of Britain's only existing private sector university, Buckingham; it had been opened for business by Margaret Thatcher. Kealey has long argued that all universities should abandon the state as paymaster, and that the American model should be adopted here.

Yet this too, appeared to be a Doctor Kealey through the looking-glass: Buckingham's ferociously libertarian principal told me that Grayling's new college "is just a bunch of opportunists trying to make some money. They are not giving up their day jobs in the academic state sector. These left-wing intellectuals will just be making easy extra money, funded by venture capitalists". But weren't Professor Grayling and his band of "left-wing intellectuals" just doing what Kealey had long urged – to emulate the American system? Not a bit of it, said Kealey: "The great US humanities colleges are entirely charitable foundations, not profit-making bodies. Grayling's lot are just going to be working to make a return for the venture capitalists backing them — and taking a slice of the equity themselves."

Those who oppose the whole idea of charging for tertiary education have been fulminating about Grayling ever since he unveiled his new project in The Sunday Times last weekend, but none of the left-wing educational establishment has been as cutting as Kealey, whom I had rung up in order, as I naively imagined, to find a countervailing voice of support.

So, who is in the right: the left-wing would-be saviour of disappointed parents of public schoolboys, or the free-market educationalist who denounces this as an opportunistic venture capitalists' scam?

The first thing to note is that this is no private sector version of Oxford or Cambridge, and not just because it will have no research function. It will be taking only about 350 students a year. It will be teaching just a handful of subjects, loosely termed "humanities", with the twist that all students will do compulsory modules in "critical thinking" and "ethics". The minimum entry requirements seem much less demanding than those demanded by Oxford and Cambridge. For example, its prospectus reveals that would-be students of economics can gain a place with nothing better than a grade C in GCSE mathematics – no A level required. By contrast, Oxford will not look at applicants for its economics and management course without a Maths A level, and the same goes for Cambridge in economics. It is this which has led one academic blogger to label this as a place for "Tim nice but dims whose parents are prepared to spend a fortune having them fall asleep listening to lectures by AC Grayling".

Yet what harm does this do? If parents wish to spend their money in this way, why shouldn't they? Grayling also has a point when he argues that there are going to be big cuts in humanities departments as a result of the Government's changes to university funding, so his college will be offering work to lecturers and teachers some of whom are about to be made redundant, and their wisdom (such as it is) otherwise lost to the academic world.

Where Grayling's model is genuinely attractive is that these lecturers will be giving one-to-one tuition to students. This is a teaching method that only Oxford and Cambridge practice and it is the single most valuable aspect of their educational offering. It is very hard for a student to bluff in such a rigorous environment and therefore encourages the detailed reading and hard work that we would want our children to undertake at university: perhaps the biggest complaint both parents and students have of universities in this country, is the lack of "face-time" with teaching staff. Grayling says that about a quarter of his intake will be poorer pupils subsidised through bursaries funded through the fees of full-paying students: if true, then it is closer to the American model and can not just be denounced as purely a device for hoovering up the cash of the wealthy whose children have failed to get into Oxford and Cambridge.

Most of the attention to this project has been given to its star names, made famous by television, such as Professors Richard Dawkins and Niall Ferguson. This is clever marketing by Grayling, whose gel-maintained big hair alone marks him out as a man alert to the significance of image. He admitted to me, however, that these famous figures will not be the ones doing the one-to-one tuition: they will just be lecturing (presumably when they can get the time from filming their latest television series, not to mention their day jobs teaching at Harvard or wherever). That might disappoint some star-struck parents, but in my experience the best university teachers are those least obsessed with building their wordly public reputation. If the New College of the Humanities succeeds in its ambition to be worth the fat price of admission, it will be nothing to do with its TV dons. Until we discover who its real teachers will be, its true value is unknowable.

d.lawson@independent.co.uk