The Universities of Oxford and Cambridge harbour many people of radical mind - Marxists of every hue, questioners of unexamined assumptions, critics of privilege, inequality, injustice in all their forms. Yet almost invariably they leave their radicalism and their fearless questioning at the boundaries of the two cities. Oxford and Cambridge themselves somehow remain immune to the searching scrutiny that their dons apply to everything else. So the Government’s decision last week to phase out college fees, which give Oxbridge pound;35 million more than other universities, is greeted as an act close to barbarism.

More than 20 years ago, I spent several weeks attempting to write the inside story of the two universities. I searched for dons who would dish the dirt and tell me stories of extravagant spending on vintage wines, outrageous prejudice against women, blacks and council-estate dwellers and, above all, the hopeless bias of the admissions tutors against state-school pupils. In any institution, you can expect to find a proportion of employees who are sufficiently disgruntled to talk in such terms. Not in the Oxbridge colleges. I cannot better what A H Halsey said to me: ‘The place engulfs you - it wraps itself around you rhetorically and architecturally.’ Now as then, the dons seem unfazed by the wholly unrepresentative character of the Oxford and Cambridge student bodies. The universities, they argue, are being asked to repair the faults of the state-school system. We should blame failure in the comprehensives, they say, not failure in the admissions offices. Since blaming state-school teachers is now as acceptable on the Left as on the Right, this position neatly sidesteps any ideological misgivings. (The much-repeated maxim that poverty is no excuse for failure, it occurs to me, is just about the smartest idea that the British ruling class has had this century.) The figures for Oxbridge entry are worth repeating. I take them from an article by Maria Eagle, Labour MP for Liverpool Garston, in the Times Higher Education Supplement of March 13 and from the (internal) commission of inquiry into Oxford, chaired by Dr Peter North, the vice-chancellor, which reported in January.

Of Oxford admissions, 43.2 per cent are from maintained schools, 46.9 per cent from independent schools. The equivalent figures for universities nationally are 81 per cent and 18.3 per cent. Students from working-class homes take 17 per cent of the Oxbridge places, against 39 per cent nationally. Put another way, one in 14 independent school pupils makes it to Oxbridge, against one in 450 comprehensive pupils.

On socio-economic background, North concluded, in typically donnish fashion, that “the data ... gives some cause for concern” but “more analysis is required before any firm conclusions can be reached.” Well, I suppose more analysis may be required of how the Earth goes round the Sun but I would have thought that the social bias of Oxford entry, which has been known about for almost as long, might by now have led great minds at least to a few working hypotheses.

The usual excuse is that a state-school pupil with a given set of A-level grades has as good a chance of admission, provided he or she applies, as a public-school pupil with the same grades. The problem is that state-school pupils with top grades are even less likely to apply than their public school equivalents. If there is bias in admissions, it reflects bias in applications.

This will not do. Injustice is no less unjust because those affected are, to some extent, complicit. Consider how the Oxford and Cambridge colleges look to an Etonian, an Harrovian or a Wykehamist. Quite possibly, a parent or other close relative will have attended; their teachers will talk about them with familiarity; they or their families will probably know a few dons socially and they can expect to go up with several classmates. To them, taking a place at Oxbridge comes as simply and as automatically as taking a job in the shipyards once did to young men on Tyneside or going down the mines did to those in Barnsley.

Contrast that with the perceptions of working-class children from northern comprehensives who may know literally nobody, even a teacher, who has spent more than a few hours in an Oxbridge college. To them, Oxbridge is alien, mysterious, socially intimidating.

In her article, Ms Eagle wrote well about all this. Nobody would accuse Dr North of writing well of the same issue (we are talking about a committee here) but, from the four-and-a-half pages of his 237-page report that he deigns to devote to admissions, he gropes towards the same solutions as Ms Eagle. These are of what I would call the touchie-feelie sort and mostly involve dons touring the inner cities to radiate warmth and explain that Sebastian Flyte is dead.

For a more radical solution, you have to turn to the foreign pages of The THES in the same issue. There, you learn that the University of California is considering a measure that would automatically give places to the top 4 per cent of students from every school in the state. An editorial points out that annual entry to Oxford and Cambridge is too small for them to offer even two places to every secondary school and college in Britain but I do not think mere arithmetic should deter us.

Numerous permutations are possible, including offering places to the best students from localities embracing three or four schools (which could be designed so that equal numbers of students were competing for equal numbers of places) or creating a scheme in combination with other elite universities such as Durham and Bristol. If Oxford and Cambridge were, between them, to offer just one place to the highest-performing student in every school or college, state or private, that teaches A-levels it would be enough to transform their student bodies. At least a quarter of the places would still be available for traditional competition, plus any of the automatic entry places not taken up. (There would need to be some minimum threshold of, say, three B grades or at least one A grade.) I doubt that this solution would lead to any significant diminution in Oxbridge standards; even if it did, the benefits in a more varied student body would far outweigh it. The effects on the school system would be extraordinary because some middle-class parents might well calculate that, if they sent their children to inner-city comprehensives, they would stand a better chance of an Oxbridge place.

I am astonished that a left-wing government did not offer a deal to Oxbridge: adopt a solution of this sort and you can keep the college fee. I am astonished that left-wing dons at the two universities didn’t mount a campaign for this idea years ago. But who’s really left-wing nowadays? No, perhaps I’m not so astonished.