John Davies explores the inner precincts of a club that likes to say no to women, the Oxford and Cambridge. What is going on behind the neo-classical facade of 71 Pall Mall, London SW1, that has united the college heads of Oxford and Cambridge in denunciation?

The answer, of course, is in the name that, although not displayed outside the building, is to be found inside the United Oxford and Cambridge University Club. For those who have missed the headlines, the protests and the letters to The Times, the problem is that the club's rules do not allow women to be full members. They can be only associate members, a status that enables them to dine and stay at the club, but denies access to its library, its bar, and its main staircase. But with the student populations of Oxford and Cambridge now about 40 per cent female, should not a club using these universities' names and coats of arms, and restricted largely to their graduates, reflect such equality?

When the two vice chancellors and the heads of some 70 Oxbridge colleges made this point last month, protesting about the club's "discriminatory policies" and resigning en masse, it was a unique occasion. Never before have heads of colleges from both universities got together to agree on a statement in this way. Even the few who did not sign, such as Somerville's principal Catherine Hughes and John Barron, Master of St Peter's, Oxford, have, in one way or another, expressed their disapproval. Hughes (a member of the non-discriminatory Reform Club) makes a habit of refusing to sign protest letters on principle, but has privately made known her opposition to the club's male bias; she has always declined to assist its annual recruiting drive among new graduates of her college. And Barron has said that he is staying to continue fighting for change.

Others such as David Butler, fellow of Nuffield College, have given up the idea of fighting from within. When in 1993 the club voted in favour of elevating ladies to full membership, there was a majority, but not one big enough to change the rules. Nevertheless some feel the club could have made some concession to sex equality. It could, for example, have allowed lady members access to the main staircase. (It could even have given men the option of associate membership.) As Sir Patrick Nairne, the former Master of St Catherine's, Oxford, who campaigned for full membership for women, says: "The committee could give a token that they understand that the world is changing." No such token has been forthcoming - indeed the club has not, as yet, responded to the college heads' protest.

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What then is it like to belong to what even Sir Patrick calls "an extremely well-run club"? As it happens, being male and holding an Oxbridge BA, the author of these words has the necessary qualifications to apply for membership. So I telephone to enquire about joining. Of course, I am told, but you need to be proposed and seconded by two members. Meanwhile, would you like to look round?

And so I do. The first person I meet is female: a receptionist crisply attired in navy blue and white. And my guide for the afternoon is a friendly middle-aged lady assistant who leads me into a side corridor, past a notice marked "Ladies' Side", towards a lift.

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Up we go to see the kind of bedroom a club member would be able to use. It is a fairly functional twin-bedded room with en suite bathroom, but with a view across St James's Park towards the roofs of Westminster Abbey and the Houses of Parliament for which an American tourist would gladly pay several times more than the Pounds 72 a night required of members.

Down to the second-floor library with "nearly 25,000" books on its shelves. Plenty of weekly and monthly magazines, too, as well as the daily broadsheets in the high-ceilinged smoking room; but, contrary to stereotype, no ageing mentors doze over the City prices. The only gentlemen to be seen are in earnest conversation or at work in the nearby Silence Library (the only public room in which it is permissable to remove your jacket).

I walk with my guide down the ladies' staircase - a privilege, as it is forbidden to unaccompanied men - look into empty meeting and function rooms; and admire the ladies' drawing room, where a small all-female group is socialising at one end. I see the television room and hear the unmistakable sound of balls hitting walls in the club's subterranean squash courts.

I am too late to be served in either the quick lunch bar or the main dining room. But I have already eaten well today: ten minutes' walk away in Mayfair, at the University Women's Club.

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Yes, I have been inside what might be considered the men's club's female - but less well known - counterpart. Indeed, club secretary John Robson calls it "a very well-kept secret". Founded in 1886, some 50 years after the Pall Mall club, and now occupying what was originally the town house of Lord Alfred Russell, this University Women's Club is altogether on a more modest scale. The entire ground floor could almost fit into the O & C's tennis-court-sized dining room, and its library, though well-used, is smaller. Despite the university in its title, members need not be university graduates. Nevertheless, the club has strong historical links with colleges such as St Hilda's, Oxford, for whom it is hosting a series of recitals to raise funds for a Jacqueline du Pre Music Building.

Other comparisons: it has 24 bedrooms to the O & C's 43, and "about 1,300" members to more than 3,500 at the Pall Mall club; its annual subscriptions range from a Pounds 25 student membership to Pounds 248 for members over 30 living within 30 miles of London. Instead of associate members, the University Women's Club has a "male dining" category (Pounds 157 a year, paid by "a very modest number".) No staircase or library is inaccessible to such men: in fact, says the club's brochures, they "may use (all) facilities except those of residence".

All the same, the corridors-of-power feel to the Pall Mall club has its allure. Could I conceivably become a member? Would it not be pleasant to stroll into such an edifice as of right, to belong there? Before I leave the O & C I am handed a list of members to assist me in seeking a proposer and seconder. From this list (names and former colleges but no addresses), I can identify two people that I know slightly from my old college. One lives abroad; the other, when contacted, tells me he is no longer a member. He failed to renew his subscription a couple of years ago, having realised he wasn't using the facilities enough to justify the expense.

Oh yes, expense: Pounds 574 a year is not as much as some other London clubs, but it is still a fair slice of an income if someone else is not paying (and it would not be tax-deductible). A pity I am not "holding an appointment or in statu pupillari at Oxford or Cambridge University", in which case I would only pay at the most Pounds 371 a year.

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And, of course, if I were a woman, I would pay even less: Pounds 212 is the highest annual subscription an associate member is required to pay (Pounds 153 if in residence at Oxbridge). If you are a female Oxbridge graduate, and it is not the library or the bar that you need but simply somewhere in Pall Mall to use as a London base, the club could be a bargain.

On the other hand, you might echo the words of University College, London, historian Kathleen Burke, who was approached some years ago by a (male) friend who belonged to the O & C and thought she might like to join. "I trotted along, but when I discovered that I was going to be allowed the television room but not the library for example . . . I decided I would not pay fees to anything that treated me as a second-class citizen."

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