Consider this for a contradiction. According to a recent survey, London is the world's most coveted place; the British capital's dynamism and welcoming approach to foreigners makes it the destination of choice for the largest number of people seeking a job abroad.
Yet at the same time, Britain is gripped by a powerful backlash against immigrants: if general elections took place today, up to one in five of all Britons could be voting for a party whose only political platform consists of a pledge to seal the country's borders against all incoming foreigners.
How can one explain this gap between a welcoming city and a hostile nation?
Simple: London is no longer representative of the country to which it serves as capital; instead, it's a city which has effectively created its own way of life, a parallel social ecosystem.
Nor is this phenomenon of the "urban bubble" confined to Britain alone, for Europe has other capital cities which increasingly also have little to do with their countries.
It is a trend which carries profound and long-lasting political implications, although few of these have been understood by Europe's current political class.
Profound differences between towns and their countryside have, of course, been a feature of European life for centuries. But at no point have such disparities been as large as they are today.
Take London, Europe's biggest metropolis, as an example. Its population makes up just 13 per cent of all UK residents, but the city accounts for a quarter of the British economy. On a per capita basis, Londoners are 30 per cent wealthier than the rest of the United Kingdom. And they are also much better educated: 40 per cent have a graduate degree, more than double the national average.
But it's the ethnic diversity of London which is most striking. Almost half of its population is foreign-born, compared with just 9 per cent nationwide. And while 95 per cent of Britons identify themselves as "white", only 59 per cent of Londoners do so.
Hands up those who can guess what's the second most widely- spoken language in London; it's actually Polish, mother tongue of no fewer than 600,000 of its residents.
Such a diversity translated into other peculiarities. Londoners buy a third of all the expensive, organically-produced food in the United Kingdom. But they have the lowest share of car ownership in the country. For most Britons, owning a home is an obsession. Not for Londoners, however, where over half of the residents live in rented accommodation.
A similar situation prevails in France, where fears that Paris would end up dwarfing the rest of the country were so entrenched that the capital city was not allowed to elect a mayor until 1977. And for good reason, since the moment the position of Paris mayor was created, everyone who ended up holding that post used it as a springboard for the French presidency.
And, as in London, ethnic diversity marks Paris apart from the rest of the country. By law, France does not collect data on the ethnicity or religion of its people, but it does have information on its residents' country of birth.
According to these statistics, over a quarter of all Parisians were born outside France, almost four times the national average.
In Germany, Berlin has long suffered from the perception that it was the source of Germany's historic ills, including the Nazis. That's unfair: most of the leading Nazis were not from Berlin and detested the city.
Still, national suspicions of Berlin and the city's painful divisions during the four decades of the Cold War have left their mark: Berlin is still poorer than other German population centres such as Frankfurt or Munich.
But Germany's capital is catching up fast, as hundreds of thousands of top German civil servants, diplomats from every nation and well-paid business executives pour into the city.
Berlin's population is already younger than anywhere else in Germany. Berlin is the city for every "alternative" lifestyle imaginable, as well as quite a few you'd never dare imagine. And, of course, it's racially diverse, with entire areas of the city dominated by ethnic Turks; overall, the city's non-German population is about 20 per cent, almost double the national average.
Apart from deceiving those who think that by visiting Paris or London they see Britain or France, do such distinctions between capital cities and their countries matter?
They do, in profound, surprising ways. First, because capital cities command many votes, control the media and are far better at articulating their needs, they skew national development priorities, by attracting a disproportionate share of investment resources.
When British politicians and newspapers complain about the woeful state of their antiquated transport networks, they usually refer to the commuter belt feeding millions into London, not to the countryside, where public transport is virtually non-existent. Vast resources are being poured into this commuter belt; as Mr Vince Cable, the British business minister, complained recently, London is "a giant suction machine, draining the life out of the rest of the country".
But other capitals also enjoy privileged attention. When French presidents dream up grand construction projects by which they wish to be remembered, they invariably pick Paris. And even the Germans, otherwise sensibly immune to the lure of their capital, could not resist lavishing many billions on sparkling new railway stations and a gigantic airport for Berlin.
Europe's megacities also tend to attract projects and initiatives which fire up the public's imagination and favourable media comments, but do little else. Bicycle projects are a case in point.
Paris and London have inspired schemes allowing people to rent bikes, and these have been touted as great projects in social mobility and environmental protection, although they remain the playthings of a tiny and unrepresentative urban elite and have next to no impact on national carbon emissions.
Europe's megacities are also breeding grounds for unique, niche politics. It's not entirely by accident that the current mayors of both Paris and Berlin are openly gay.
For although being gay has long ago ceased being a obstacle to politics in both countries, sexual preferences are elevated to the status of a distinct advantage in Europe's cosmopolitan cities. "I'm gay and it's good that way," the keynote phrase which a young Mr Klaus Wowereit uttered before he first got the job of Berlin's mayor in 2001, became so popular that it was even copyrighted.
"Flower power" politics of this kind are mostly harmless fun. But they also tend to reinforce the disenchantment of voters beyond capital cities, who have other preoccupations than speculating about Mr Wowereit's taste in neckties, or London mayor Boris Johnson's latest dalliance with an occasional girlfriend.
Yet the most enduring impact of Europe's megacities is that they tend to lull leaders into a false sense of security about the very nature of the societies over which they rule. All European politicians know that their capitals are not representative of their countries. But all are human, and they cannot avoid being influenced by what they see daily.
And what they encounter in places such as London, Paris or Berlin is unique: cities in which ladies covered in forbidding veils walk next to young girls wearing practically nothing apart from tastefully placed tattoos, public spaces in which people of all races drink the same skinny cappuccino with soya milk, city markets in which not only the merchandise but also the people are multi-coloured.
All this fosters the impression that race relations are far better than they really are, thereby not only lulling politicians into a false sense of security, but also encouraging them to believe that those who oppose multiracial societies or further immigration are just some insecure individuals, suffering from a powerful and irrational fear.
The tendency to portray supporters of populist parties - especially anti-immigration parties - as simpletons is invariably combined with a view of the parties themselves as cynical exploiters of ordinary people's stupidity; Europe's megacities have persuaded politicians that their societies can be both successfully multi- ethnic and peaceful, an assumption which is by no means proven.
Some countries have tried to compensate for this overpowering influence of capital cities by dispersing government services to other parts of the country. But this is an expensive task, and it almost never works as intended.
So, European politicians are ultimately condemned to live in such bubbles; the only thing they can do is to try to remember that what they see on their streets bears little resemblance to reality.
Or they could move their capitals to new locations.