There has been such enthusiasm for Barack Obama in Britain that it is strange no one seems to have looked into his feelings about Britain. It is perhaps natural for his foreign supporters to assume that their adoration of the president-elect will be returned, but there is no indication that Obama is at all Anglophile or interested in the "special relationship" in any profound way. All indications seem to be that he will be much more interested in winning the affection of what used to be called the Third World than in paying attention to the adoring electorates of Western Europe. Moreover, it's possible that he might look past all the British talk about how wonderful it is to have a black man in the White House and notice with distaste how little minority representation there is in British public life.

It will certainly be interesting to see if his election prompts a genuine and profound shift in British attitudes to America. Many people believe that the Bush presidency has deepened anti-American feeling in the UK, though the gloating reactions to the 9/11 attacks by the likes of Cambridge professor Mary "they had it coming" Beard might imply that anti-Americanism was already established as a virulent force in establishment Britain long before W. arrived in the White House. You can quite easily detect deeper currents of hostility or jealousy or disdain that have little to do with any particular administration, everywhere from newspaper headlines ("Yanks Kill Our Boys" about a friendly-fire accident in Afghanistan) to the way that popular slang has evolved: it's fascinating, for example, that "cowboy" in Britain is a pejorative adjective implying carelessness, lawlessness and lack of integrity, whereas in America its connotations are almost all virtuous.

Some clue to the way things might turn is offered by the spate of books, and radio and television programmes, prompted by the imminence of the American presidential election. They purported to examine the United States, her character and her role in the world; many of them were presented by media celebrities like Stephen Fry, Simon Schama and Jon Snow. Some, like Fry's, were genuinely affectionate. Others were patronising or verged on the hostile. It was probably telling that a BBC Radio 4 debate about the greatest influences on America included the radical leftist Howard Zinn but did not seek to balance his extremist vision of America as an agent of evil with an equally fervent pro-American booster.

Although working-class Britons tend to be much more pro-American than their supposed betters, being condescended to by Britons is an occupational hazard for Americans abroad. I personally am usually spared it because I sound English and am only half American anyway. On the other hand, my accent means that I sometimes get to hear anti-American rants that might be withheld if there were an obviously American person in the room. "How can you bear living there?" I was once asked at a dinner party when visiting from New York, where I then lived. "It's all so Styupid!"

Of course, devoted hard-core anti-Americans of the Left or the Right won't hesitate to tell you what they think of the US even if you are their or somebody else's guest. British anti-Americanism of that sort tends to be far too obsessive and quasi-religious to be held back for reasons of good manners. And when you are confronted by someone who is willing to believe anything bad about America, you are likely to find that rational polite discussion about the subject is not really possible. Mind you, this is also true of American anti-Americans of the Chomsky type who need to believe that there is no evil anywhere that is somehow not the fault of America (or perhaps Israel).

What I didn't say but should have said to the man who pronounced "stupid" in a Pythonesque way is that America isn't really stupid, but sometimes seems so because it is different in ways that you may not understand or find appealing. As de Tocqueville noted, America is an extraordinarily democratic and demotic country in which the feelings and tastes of ordinary people set the tone much more than they do in the UK. (This is one reason why inarticulate men who would not shine at smart dinner parties can be elected president.) In America if a massive majority of people believe in the death penalty, then the dealth penalty remains legal, even if many people in the equivalent of the British chattering and political classes are horrified by it. It is a polity that for historical reasons has often chosen a different compromise between liberty and security, hence its peculiar gun laws. It's a society which has long fostered a sometimes unattractive conformism - including strange Soviet-style rituals like the Pledge of Allegiance - in order to counter the potentially divisive effects of mass immigration, unbridled markets and internal migration. Arguably, those rather un-Anglo-Saxon measures have worked very well: people from the most distant and different societies become patriotic Americans very quickly. You don't find many second-generation Arab-Americans or Pakistani-Americans drawn to violent jihad against their own country. On the other hand, I can understand why the sort of Briton who is attracted to or nostalgic for a traditionally hierarchical society or who has an aristocratic or Left-aristocratic contempt for commerce is likely to loathe American culture.

I am, however, often struck by the gap between what Britons think they know of America and the reality. Take the matter of race. Many British pundits apparently think that America in the 21st century is Alabama in 1963 writ large. Perhaps the fact that America has elected a black president (when enlightened Britain can only manage a handful of MPs) may shift this perception, but it is one that should have shifted long ago. The US, after all, has had two black secretaries of state - in a conservative republican administration. It had its first black Supreme Court justice, Thurgood Marshall, in 1967 and its first black general as far back as1954. It has had black CEOs of Fortune 500 companies like Kenneth Chennault of American Express, Stanley O'Neal of Merrill Lynch, Ronald Williams of Aetna and Richard Parsons of Time Warner. It will be a long time before Britain or any Western European country with a large ethnic minority population can even approach such achievements.

False familiarity is the besetting sin of British commentary on America, whether on the TV and radio or around the dinner table. Many people seem to think they know the US because they watch a lot of American TV (even if they affect to despise it). Of course, they are generally sensible enough not to assume that the programmes they watch present a completely rounded picture of the US - they are aware that crime scene investigators, despite their dominance on the box, are actually a very small percentage of the population. They may not be aware, however, of social realities that aren't important to the makers of TV police series. To appreciate just how absurd it is to draw one's sense of America from US TV, you just have to imagine the picture of Britain that an American might come up with if he or she built it up from episodes of Spooks, Little Britain, EastEnders, The Glittering Prizes and Casualty, with its relentless whining about NHS cuts.

False familiarity often leads to a kind of laziness in British approaches to American culture. You can see or rather hear this most obviously on the stage. Like my American father before me, I often find it unbearable to watch American plays performed in the West End or to listen to English actors mangling American writing on Radio 4. There are notable exceptions, like Emily Mortimer and Hugh Laurie, but even our best actors seem to think there is a single received "American accent" and then come out with some awful combination of Brooklyn, Alabama and Texas.

You can find a similar disinclination to do American homework in film and book criticism. It was telling, for instance, that almost none of the Britons who reviewed Philip Roth's latest book Indignation realised that the "Winesburg College" at which much of the novel's action takes place is a) fictional and b) a deliberate and freighted reference to one of the classics of 20th-century American fiction. Any American literature student with even a basic acquaintance of the US literary canon would have at least heard of Sherwood Anderson's Winesburg, Ohio and probably know that its component stories are peopled by Midwestern grotesques.

This is not to say that Americans don't get British cultural references horribly wrong. Woody Allen's recent films made in London are all but unbearable in their crude and clueless take on English class and English manners. Allen radically overestimates his understanding of English subcultures and overestimates their similarity to those he knows in America (WASPs are not the same as Sloanes, even if they do have much in common). This may indicate a generational shift; earlier generations of American writers and film makers were more likely to "get" things English.

Certainly my own father, the exiled American filmmaker Carl Foreman, had a remarkable understanding of the kind of cultural subtlety that Allen misses. This was at least in part because like so many Americans educated before the Second World War, he was steeped in British literature. If you had read enough Dickens, Hardy, Fielding, Austen, Thackeray, Lawrence and so on, you were much more likely to notice and understand the cultural texture of Britain in the '50s, '60s and '70s. From the day my father stepped off the boat in 1953, he was stunned by the familiarity of places, phrases and social types that he had known only from books, whether he was visiting the East End, a Welsh mining village or the House of Lords. Today, it's hard to imagine a state-educated American whose schooling would have been so extraordinarily anglophile or a course of reading that would enable him immediately to understand a society that has changed so much in such a short time that even the natives are confused by it.

Of course, certain kinds of Americans, especially members of the left-leaning intelligentsia, can be every bit as ignorant of America and just as prejudiced or deluded about it as the silliest British newspaper pundits. I've heard plenty of American foreign correspondents and even State Department diplomats tell me that they could never live in America again, the implication being that they are now simply too cultured and sophisticated to live among their provincial, hamburger-eating fellow countrymen. And even within the US there are many upper-middle-class New Yorkers, Bostonians and Los Angelenos who like to characterise "flyover country" as a terrifying haven for inbred bigots and ignoramuses. These people tend to have little first-hand knowledge of Middle America. They know rural America from Deliverance, Blue Velvet and Easy Rider. They know how hellish suburbia can be from Desperate Housewives and the even more ridiculous American Beauty. Indeed, I've often been struck by the way British students on their gap year visit more American states than supposedly well-travelled Manhattan sophisticates do in their whole lives. If they had, they might be struck by the friendliness, decency and humility of Middle Americans. If some New Yorkers and Los Angelenos believe that everyone in the hinterland dons sheets and burns crosses of a Saturday night, it is because much of what they know about such Americans comes from television programmes made by people with the same prejudices. The idea that the heartland is both bland and dark, or dull and terrifying, makes a certain kind of East Coast urbanite feel immensely superior. These people have arguably been proved wrong by the election of Obama, and it may be you will hear less jokey talk about why New York should form a new, separate country.

I'm not sure if anti-American Americans are more common than anti-British Britons, but they are probably more dominant in academia and the media. Certainly they are very powerful in Hollywood. It's telling that the latest Bond film, Quantum of Solace, which runs counter to the traditions of the previous Bond films and books by putting the CIA on the side of the bad guys, along with multinational corporations, etc, and implicitly supporting the likes of Hugo Chávez, was largely written by the left-wing American (albeit Canadian-born) screenwriter Paul Haggis.

Stereotypes can persist long after the inspiration for them has disappeared. In Britain you still hear talk about fat American tourists even though obesity has become a problem here too. In America people still expect British visitors to be well-mannered and cultured, despite the arrival of the loutish British equivalent to the ugly American. In general, both Britons and Americans expect the other to be more like them. This can deepen the shock when they encounter some cultural differences they might not even be aware of if they were visiting a European country whose language they didn't speak fluently. This doesn't in any way diminish all the many profound things our two nations have in common. It's like the differences people encounter within their own family. On the other hand nobody appreciates America like a Briton who loves it, and no one loves Britain more than Anglophile Americans. Thank goodness, there are plenty of both.