Some years ago, not long after we saw the looting and burning of Baghdad together, I went with my Iraqi friend Ghaith for lunch in Broadway Market, in Hackney, one of the many parts of London where gentrification of a previously run-down area has been going on for years. The street was, and is, lined with cute shops, bars and restaurants for attractive, trendy, second-generation creative and media types. It has become one of the poles towards which the compass needles of estate agents and fashion-conscious yuppie couples quiver. There is no point in looking to buy a house nearby unless you have at least half a million pounds at your disposal. When Broadway Market actually becomes a market on Saturdays it is as if the council-owned tower blocks and estates behind, around and in between the gentrified patches, where less well-off and poor people live, belong to some other dimension.

As Ghaith and I walked down the street a disturbance began. A group of about thirty young black kids were moving together, looking anxious and excited. Some had makeshift weapons in their hands, poles and lengths of broken-off wood. After a moment, between a gap in the shops that looked through to the base of a tower block, we saw the reason for their anxiety – two tiny figures on bikes, dressed in black, hooded and masked. As we watched, one of the figures reached into the pocket of his hoodie and lifted – just enough to show – a hand gun, spreading panic among the larger group.

The trouble subsided as quickly as it began and the participants dispersed before the police arrived. Throughout the episode, a young, casually dressed, thoughtful-looking white couple sat at a table outside a wine bar, watching and sipping white wine. The neck of the bottle leaned, misted with condensation, from the rim of an ice bucket on the table. The couple didn't look concerned that the gang confrontation or turf battle, whatever it was, would affect them; the feuding kids didn't seem to see them, either.

This is the reality of multicultural London. It is not a melting pot. It is a set of groups that are rigidly self-separated by race, language, religion, class, money, education and age group, who have not only come to an unspoken agreement that they will not mix, but have become complacent that this agreement will not and need not be challenged. As Slavoj Žižek has written in his book Violence,

Today's liberal tolerance towards others, the respect of otherness and openness towards it, is counterpointed by an obsessive fear of harassment. In short, the Other is just fine, but only insofar as his presence is not intrusive, insofar as this Other is not really other... My duty to be tolerant towards the Other effectively means that I should not get too close to him, intrude on his space. In other words, I should respect his tolerance of my over-proximity. What increasingly emerges as the central human right in late-capitalist society... is a right to remain at a safe distance from others.

Bring on your exceptions. Bring them on by the thousand, by the ten thousand. But the truth holds: this is not the mixing city its liberal inhabitants would like to think it is. Loving the cultural diversity of London as a spectator-inhabitant is not the same as mingling with it. The yuppies don't go to the white working-class pubs, and the white working class don't go to the yuppie pubs. The Muslims don't go to the pub at all and the post-Christians don't go to the mosque or the church. The young don't mix with the old. You don't marry outside your income and education group. Parents segregate their school-age children by class and race.

I live in Mile End, about halfway between the site of the Olympics and the closest proper looting spree that I heard of, in Bethnal Green. It was quiet here last night (I haven't heard of any trouble in Broadway Market, either). On the face of it my area's mixed, ethnically and socially. They've just built a new Hindu temple on Rhondda Grove. The students at the girls' school across the road are almost entirely Muslim. The church along the way which would, I assume, be derelict otherwise, has been taken over by a black congregation. Middle-class white atheists like me sail around on our bikes to buy our coffee beans in Broadway Market or Victoria Park Village; there are Georgian houses round the corner that a million pounds wouldn't buy you, and there's the eastern stretch of Roman Road, with pound stores and pawn shops and elderly geezers who never made it out to Essex and a market that makes Albert Square look posh. But this isn't mixing. It's the ingredients for something – nobody knows what – laid out side by side and not being mixed, not touching.

Jan Morris offered a partial defence of the British Empire as an unarticulated effort by Britain to engage with the world – a mutual introduction by conquest. Looting a shop and then burning it down, ignoring the people living in the flats above, can't be excused or accounted for as a way for a particular group to say to London, 'Hi,' and yet that is one of its effects. 'We are here; we exist; we have actual weight; we can break the deal and cross into another zone than ours.' The response of the rest of London to this kind of introduction will be harsh and sceptical, and when it is over, the question will remain unanswered: how, and by what agency, to bring the diverse groups of a city divided by age, class, education, money, race and religion closer together when they are so conscious of their own differences that, left to themselves, they prefer to watch each other from a distance?