Melanie McDonagh: The real route to popularity – if you want to get ahead, get a cat

Larry's arrival at No 10 tells us that Cameron really means business

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Larry, the new cat at 10 Downing Street, is said by a spokesman to have a "strong predatory instinct". Should be right at home, then. Indeed, Larry showed a spirited approach to the media when he clawed a reporter who tried to get him to pose last week; later he was pictured walking calmly along the Cabinet table, picking his way among the papers. For a cat from the Battersea Dogs and Cats Home, he seems utterly unfazed. But then, that's cats for you: they do the intimidating.

Larry follows a line of feline inmates of No 10, from Humphrey of blessed memory, who walked into Downing Street uninvited and was given a home by Margaret Thatcher then retained by John Major, to Ramsay MacDonald's Rufus of England, a good mouser who was nicknamed Treasury Bill. All we need now is for Samantha Cameron to be pictured cuddling Larry: the great function of pets in politics is that they humanise power. We would think better of David Cameron if he turned out to be fond of Larry, just as an affection for Humphrey almost redeemed Margaret Thatcher.

The thing cuts both ways: Cherie Blair's reputation never quite recovered when the rumour got round that she had got rid of Humphrey because he was "unhygienic". Not An Animal Lover is a bad reputation to have in British politics; Ed Miliband, if he had any sense, should by now have got himself a cocker spaniel and professed his devotion to it.

The burning question is: what are Larry's politics? Last week The Guardian claimed that cats are natural liberals, or if not liberals at least nihilists and anarchists. Dogs, it said controversially, were Tories, being pack animals who do what they are told. Well, possibly.

Certainly, cats are non-conformists, but you could argue that they are natural aristocats too. If you go to the British Museum, you find that ancient Eygptians gave them mummies almost as grand as those for humans; indeed Bastet, the cat goddess was the patroness of domestic cats. It's fair to say, however, that their status in modern Britain is humbler. Cats are not the natural pets of grand Tories; dogs are. You'd expect David Cameron's nanny or housekeeper, not the Prime Minister, to have a cat. Dogs, you see, are associated, among other things, with country sports; a good gun dog is priceless.

In grand country homes, it's the dogs that have the life of Riley, loafing around in front of the fire. And not midget dogs either; we're talking retrievers, labradors et al. Big dogs are, by definition, high maintenance; they also call for you to have a sublime indifference to dog hair and muddy paw marks all over your jumper, which country people do.

The Queen has her corgis; Princess Anne – wouldn't you just know it? – had her bull terrier, which killed one of the corgis and attacked a couple of children. You need space for a big dog, which means that the urban masses, living in flats, are almost by definition excluded from owning one. (I belong to this category of the canine dispossessed; I gaze hungrily at other people's spaniels the way childless women sometimes look at other people's babies.)

The old working-class attachment to terriers – dogs that you could ferret with – is almost exclusively associated with house-ownership and, by extension, the possession of at least a back yard. The class associations of dog-ownership is, of course, complicated nowadays by the sinister development of gangster dogs, the Dobermanns and Rottweilers who are trained by their male owners to be a kind of extension of the very worst aspects of their own personality. And dogs being dogs, if they are trained to be vicious attackers, that's how they will turn out. The class war being played out in Britain's urban parks isn't so much between nobs and plebs as between mad, bad, chav dogs and the respectable, middle-class dogs they terrorise.

Yet the relationship between dogs and owners isn't quite so straightforward. As fans of the Disney version of 101 Dalmatians will recall, there is all too often an uncanny resemblance between dogs and their owners, or if you prefer, dogs and their humans. The question remains: are we attracted to an animal who resembles us, or do we come to resemble our pets? The brilliant film comedy Best In Show, about the passions and rivalries in the dog world, suggested that dogs' temperaments could impress themselves on owners; one couple turned from rabid neurotics to sensual extroverts simply by swapping their uptight dog for an outgoing one with a high libido.

Deep waters, these. Religion, obviously, is bound up with the pet question. Catholics and Protestants have strong cultural associations with dogs; many clergy are devoted dog-owners. But Judaism has a slightly more distant approach; the only reference in the Old Testament that is anything but derogatory is in the Book of Tobit, (a book of the Bible that Catholics accept as canonical but Protestants do not).

But it is Islam that really has a problem, culturally, with dogs, regarding them as ritually unclean. Devout Muslims generally steer clear of dogs, although Islamic tradition insists that animals be treated humanely. Indeed, one irate dog walker in Holland Park, London once told me huffily that when her over-exuberant dog approaches Muslim families, their reaction is horror and disgust. She could hardly have been more annoyed if they had spurned her baby.

Indeed, the dog question is one that probably poses a greater threat to cultural integration than the burka; the notion that Muslims do not like dogs, and even treat guide dogs with reserve, presents a formidable obstacle to multiculturalism. However, in general, Muslims do like cats, as anyone who has been to Islamic societies will testify. One of the more appealing stories about Mohamed is that he once rose for prayer only to find a cat sleeping on his arm and, rather than disturb the animal's repose, cut his sleeve off to let it sleep on. By many accounts, he had a cat of his own, Muezza. So Larry may play well with Muslim voters.

Barack Obama famously acquired a dog rather than a cat, following a hallowed precedent of previous presidents. Bo, a Portuguese water dog, was a present from Senator Ted Kennedy. Michelle Obama has declared: "I love that dog." A prudent move. In fact, the Obamas are breaking with convention here, as in so many other aspects of the presidency. It was a hoary old tradition that black Americans did not care for dogs, because of a dim ancestral association with the dogs that slave-owners used to track down runaway slaves. By embracing Bo, the Obamas have reclaimed dogs for all ethnicities. Bill Clinton, a dog man if ever there was one, had a brown labrador called Buddy. He had a problematic relationship with Socks, the White House cat. Mind you, so did Chelsea Clinton. One of the very few raps attributed to her in the White House runs as follows: "Socks sucks/ I hate that cat. Socks sucks/More than Gatt." Bad politics, that.

In fact, is there such a thing as a dog person or a cat person? It is one of the great dividing lines within humanity, which makes other differences, such as politics and religion, seem merely trivial. Personally, I think you can go both ways: I am fond of cats and I love dogs. And I find it impossible to dislike anyone who is keen on cocker spaniels.

It may be that dog-lovers are emotionally needier; dogs will give you unconditional love in a way that cats don't. But what's not to like about unconditional love?

Cats are for sensualists; the sensation of stroking a cat's coat and eliciting that boiling-kettle purr, is famously calming. If David Cameron can contrive to have himself pictured with Larry on his lap in place of a red box, the nation will, I think, feel that little bit more at ease. For cats and dogs care as little as babies about our politics, our background. They see right through to the inner man. It's one reason why politicians, if they have sense, tend to go for pets. If their dog or cat loves them, voters reason, why, they can't be all bad. Perhaps George Osborne should buy an entire menagerie.