LIBERAL internationalists in Britain have plenty of reasons to despair over the vote to leave the European Union. The economy will surely weaken, whether it dips into recession or just grows more slowly over the next few years. The government will be so preoccupied with divorcing the EU that it will have little energy left for, say, reforming criminal justice or building new airport runways. Neither the government nor the Labour Party is led by a liberal. But what really offends liberals—particularly in London—is the thought that Britain is bound to become less tolerant, less international, less diverse and as a result less interesting. In this respect the worriers are wrong.

The map below, produced by the Centre for Cities at the London School of Economics, shows both why liberals are anxious and why they need not worry so much. As a magnet for immigrants, London has no rival in Europe. Not only does it contain many more foreigners than any other city (which partly just reflects London’s size), it also has proportionately more immigrants than almost anywhere else. Next to London, famously cosmopolitan cities like Paris and Berlin are actually rather homogeneous. London’s only competitors in the diversity stakes are smallish cities like Lausanne in Switzerland. And many of Switzerland’s immigrants are from neighbouring countries, especially Germany. London’s come from all over the place.

If national diversity is the goal, Britain’s capital has an enormous head start. And it is unlikely that even Mrs May, who detests mass immigration, could do much to hobble it. True, some French and Swiss bankers will probably push off when the EU moves to undermine London’s financial services (as it surely will). So will some other workers in footloose businesses that rely on skilled immigrants: don’t expect London to remain a fintech hub, for example. That is a shame. But these people are a tiny sliver of London’s immigrant population. Almost all the others will stay put.

They will remain partly because they have British children. In 2014, 27% of babies born in England and Wales had immigrant mothers, up from just 12% in 1990. Polish women had more babies than any other immigrant group: they accounted for 3.2% of all births. Pakistanis were second, followed by Indians, Bangladeshis and Nigerians. Many other babies who were born to British women had an immigrant father. Soon these babies will be in school and their parents will be pinned to Britain.

Even if immigration were suddenly to stop, Britain would become more diverse. Immigrants have slightly more babies—their fertility rate in England and Wales is 2.1, compared with 1.8 for the natives. And diversity will spread. Immigrants tend to arrive in big cities and gradually move out, seeking bigger houses that they can afford. Between 2001 and 2011 (the last two census years) the proportion of black Africans in England and Wales who lived in London fell from 80% to 58%—a staggering exodus. Provincial towns such as Milton Keynes are rapidly becoming more racially mixed.

And although immigration will surely slow down—a consequence of economic weakness as much as government policy—it will not stop. No developed country can shut the door on all refugees, all foreign husbands and wives, and all skilled workers. Britain is highly unlikely even to keep out the unskilled. Though they have been largely forgotten, many foreign workers toiled in the fields of Lincolnshire and the food-processing factories of the Midlands even before Britain opened its doors to east Europeans in 2005. Some of those workers came in under a programme known as the Seasonal Agricultural Workers Scheme, or SAWS. If Britain ends up leaving the European Economic Area and shutting down automatic free movement from the EU, farmers will lobby hard for a SAWS 2. They will undoubtedly get their way.

As immigrants and their children multiply and disperse, the Britons who most dislike immigration will disappear. Old Britons voted to leave the EU in far greater numbers than young ones; the uneducated were much keener on exit than the educated. Britain is growing older, but this particular cohort of thinly educated old people (call it the UKIP cohort) is ageing out of the population. It will be replaced by successive cohorts that are more ethnically diverse and highly educated. In the early 1960s only 15% of school children got at least five good O-levels; today more than two-thirds get at least five good GCSEs and almost half of young people go to university.

So Britain will gradually change. While you wait for that to happen, though, remember that it is not at present a racist or intolerant country. Britons (including old, white, working-class Britons) might dislike immigration, but they tend also to dislike racism and discrimination. Eurobarometer, which obsessively polls Europeans on their prejudices, consistently finds that Britons are unusually relaxed about the idea of having a non-white political leader or non-white co-workers. The most recent poll, in 2015, found that only Swedes were as calm as Britons at the prospect of one of their children dating a Muslim.

The vote to leave the EU was not a nativist revolution, as nativists fervently hope and liberals fear. It was more a desperate lashing out against the inevitable transformation of British society—the past kicking against the future. The kick hurt a lot. But the fight only ends one way.