What is it about TV contests that causes otherwise placid souls to steam from all orifices? No sooner have handbags stopped swinging over the John Sergeant Affair on Strictly Come Scratch Your Eyes Out Duckie than a froth of indignation rises around, of all things, University Challenge. Why oh why, frets Rachael Jolley in a feisty New Statesman article, are Oxford and Cambridge allowed to enter dozens of teams (ie, one for each of their sometimes tiny colleges), when massive and very distinguished “red brick” universities such as Birmingham and Bristol are confined to one each? It's not a level playing-field, is it?

That's undeniable. The format gives Oxford and Cambridge 30 more chances to shine, and 30 times as many name-checks on prime time TV, as any other university. But does that matter? If you had to rank the inequities of modern Britain from 1 to 1,000, the Oxbridge skew-whiffery of University Challenge would surely come in at around No 997.

That's what I imagined anyway. But of course I went to Cambridge. (There! I've complied with the 30-second Rule: the theory that half-a-minute is the maximum time Oxbridge graduates can go without telling you which university they attended.) What I've found over the past few days is that the University Challenge bias does indeed irritate lots of people. It's not that they give a stuff about that programme. It's what it symbolises. This blatant favouring of Oxbridge, they say, is typical of the media world in general.

I can't disagree. There are fewer than half a million living Oxbridge graduates, yet it sometimes seems as if all of them work for the BBC. Except that this would be impossible - because who's running the newspapers, the Government, the legal profession and the City? Britain now has scores of universities (and more are on the way, in such unlikely places as Corby, Basildon and Crawley, thanks to a government plan ironically called University Challenge). They turn out thousands of high-flyers. Yet most top jobs, and most fast-track openings at the bottom, still go to Oxbridge types. On merit? Or on sight of the old blue tie? You have to wonder.

One way of looking at this is to rejoice that an educational system so wonkily constructed on an unbridgeable apartheid between “haves” and “have nots” that is first imposed on kids at the age of four, does eventually turn out a ruling-class capable of cocking up the country with confidence. Oxford and Cambridge are adept at arguing that it isn't their fault if more than 40 per cent of their entrants still come from private schools. They must take the best. If we want a more egalitarian Oxbridge, the answer (they say) is to haul up standards in state schools.

That argument is valid. But it misses an essential point. One reason why bright state-school pupils don't get into Oxbridge is that they don't apply. Their teachers are often hostile to the very mention of the terrible twosome. They have no personal links. Parents feel intimidated, and often fear that the expense of the Oxbridge high-life will be crippling. No wonder that sixth-formers believe Oxbridge to be a posh enclave for posh kids. They think they would be socially and financially embarrassed if they went there. And photos of the Bullingdon Club in full Brideshead fig don't exactly reassure them. Academic factors won't even come into it. Able state-school kids (my children included) opt for the likes of Warwick, Manchester, York or Reading. They imagine that good degrees from those fine universities will be just as acceptable to employers. Only later do they find that, in some professions, they are wrong.

Last year a comprehensive-school headteacher I know - keen for his best pupils to apply to Oxbridge, and aware that nobody on his 120-strong staff had first-hand experience of either place - asked me to talk to the sixth form and dispel their misconceptions. I started by playing a word-association game. “If I say Oxford or Cambridge to you, what's the first word that comes into your head?” I asked. The answers were: rich, elite, boat race, ancient, crusty, bow-ties, boring, posh, snobby and exclusive. I can't kid myself that the responses would have been much different an hour later. But at least I think I persuaded them that ownership of a dinner jacket isn't an obligatory entrance requirement (although, come to think of it ...).

Next month Cambridge launches its 800th anniversary jollies. Of course it's a nonsense that it was founded in 1209. The hilarious truth, in such a renowned place of learning, is that nobody has a clue when the first primordial port was passed round the first High Table. Perhaps they should try carbon-dating some of the dons.

Yet this concocted octocentenary has at least given the university an excuse to run a £1 billion fundraising campaign. That's seen as vital if it is to compete with Yale, Harvard or any of those other vulgar, johnny-come-lately American establishments that enjoy endowments of billions.

But this particular graduate would be grossly disappointed if the celebration became all about securing Cambridge's place in the super-league of scholarship. Just as important (perhaps more so, politically) is the need for the university to address the image issues that cause such resentment in its native land. Yes, Oxbridge is making more effort these days to create bridges with state schools. But as I found, there's still a mountain to climb. And both universities must advertise far more widely the bursaries available for impoverished students, so nobody can mistakenly think that they “can't afford” to study there.

What's most needed, however, is a change in the attitude of Oxbridge graduates. Alumnal pride is fine. The chauvinism that underpins the self-perpetuating, self-regarding Oxbridge oligarchies in British life is not. Confining Oxford and Cambridge to one team each on University Challenge may seem trivial. But, as Mao said, every journey begins with a symbolic first step.

Anyway, won't it be funny when the combined Oxford team gets knocked out by the new University of Basildon?

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