For a glimpse into how successful cities evolve, take in the view from the riverside office of London's mayor. High above the Thames, Ken Livingstone enjoys a panorama spanning 2,000 years of crowded history. All around, the survivors of catastrophic fires, wartime bombing and the wrecker's ball jostle for space with monuments to London's new prosperity. Just across the river, the medieval Tower of London recalls the city's past as a seat of power. To the east, the former Docklands, now home to some of Europe's grandest companies, conjures up its present as a gateway to the world. And a thicket of towers, soaring above the skyline, testifies to the status of Europe's largest and most vibrant center of world finance.

And London's work isn't done. At 7.3 million, its population is just short of the combined total for Rome, Paris, Vienna and Brussels. During the last 15 years it has added as many citizens as the entire city of Frankfurt. Indeed, this is the only major European capital that's actually growing, a favored destination for work-hungry migrants from around the globe. By 2016, according to forecasts, London will gain 810,000 more people.

All that makes the city a developer's Klondike. A score of new megaprojects are on the drawing board. Among them: a landmark 300-meter glass pyramid, billed as the tallest building in Europe, at the foot of London Bridge; a 10 billion pound rail link across the heart of the city, and the wholesale redevelopment of derelict tracts of East London to make space for the new Londoners. Remember the Millennium Dome, Britain's big gesture to the new age? A new settlement of 10,000 homes is rising in its shadow. By midcentury, tens of thousands could be living in the Thames Gateway, a string of new communities that will rim the river for 65 kilometers downstream to the sea. "Some cities capture an era--Paris in the 19th century, or New York in the 1950s and '60s," says Livingstone.

Now it's London's moment--not some cool Britannia fad, fed by a few hot bands or hip designers, but a wholesale reinvention. More than any other European capital, London thrives on the outsiders it welcomes in. Almost a third of today's Londoners were born outside the country. During the past year alone, tens of thousands of East Europeans have come to the city after Britain opened its borders to workers from the new member states of the enlarged European Union. More than 50 separate national or ethnic communities are scattered across a metropolis that sprawls over an area twice the size of New York's five boroughs. Some 300 languages are spoken, from Acholi to Zulu, all linked (and this is key) by the global lingua franca, English.

Workers in countries like Germany oppose an influx of cheap labor from Europe's newly expanded east. Even in Britain fears over run-amok immigration figure large in the current election campaign. The opposition Conservative Party's manifesto, published just last week, calls for "secure borders" and "controlled immigration." Tories say that means putting an annual cap on immigration and establishing a points-based admissions system--effectively screening undesirables. "It's not racist to want to limit the numbers," says party leader Michael Howard, himself the son of Jewish immigrants. "It is plain common sense."

But that ignores the secret of London's success. As Livingstone sees it, the Tories' extremist right-wing politics threaten to undermine the very essence of modern London--the engine that powers not only Britain's prosperity, but much of Europe's. "The truth," he says, "is that immigration is a way of life. Jewish, Irish, Asian, Caribbean, East European--each new wave has enhanced London as a global city."

Past generations of megacities rose or fell depending on their access to resources or trade--coal mines and rail hubs. What counts today is the new global class of knowledge merchants, the folks with new ideas to share or sell. "Urban economic success really depends on smart, entrepreneurial people," explains Harvard professor Edward Glaeser. "Cities have recently succeeded because urban density can facilitate the transmission of ideas." Like New York (and few, if any, other cities), London provides the right environment for these people: a relatively compact layout, a vibrant mix of cultures and a service industry fueled largely by immigrants. It is one model for the 21st-century metropolis.

London's particular alchemy has little to do with deliberate policy. For much of the 1980s and '90s, the city survived without any form of central planning. London has grown haphazardly by fits and starts shaped by global trade and economic trends. Spasms of unplanned large-scale immigration are thus as much a part of London's heritage as the double-decker bus or the black cab. For hundreds of years the city thronged with economic migrants or fugitives from religious persecution on the Continent. In the 19th century its population leapt sixfold to 6 million, including a flood of largely Jewish immigrants from Eastern Europe and Russia. The post-war decades brought another mass influx from India and Pakistan as well as the Caribbean.

Diversity is both symptom and cause of the supercharged London economy. The city must attract immigrants to stoke that growth; the immigrants want the jobs that a flourishing London can offer, whether they're 1 million-pounds-a-year Japanese bankers or Polish art historians ready to scrub floors for 7 pounds an hour. "This is where I can make something of my life," says 32-year-old Carlos Cabral from Mozambique, now running a Portuguese deli. Without the migrants, London would be shrinking, not booming.

That experience has helped to instill a basic tolerance. Londoners have learned to live with--and sometimes relish--cultural differences. "What makes us different is that we love diversity. We celebrate it," says Tony Winterbottom of the London Development Agency. Londoners don't suffer the overt racial tensions to be found in Los Angeles, Paris or Berlin. Indeed, the potpourri of cultures is an attraction in itself for those fed up with life in the suburbs, or in blander European cities. Urban centers have shed some of their 1960s associations with crime and grime; today, they offer what a new generation most prizes: high-end urban amenities, shorter commuting times, more work and more opportunities for play. London's cosmopolitan feel is crucial to its prosperity.

The city has other advantages. Begin with the famous big bang of 1986, the deregulatory splurge that opened up the city's fusty financial services and let rip the forces of global capitalism. Foreign players, impressed by London's light-handed approach to regulation, snapped up the grand old names of British finance. The doomy predictions that Britain's decision to spurn the euro would cost London its position as Europe's financial capital have proved plain wrong. Yes, Frankfurt is home to Europe's central bank, but it's London that calls the shots. Mighty Deutsche Bank may be headquartered in Germany, but its big decision makers are in London. These days more euros are traded daily in London than in the rest of Europe combined.

With the big players comes the chance to make big money; one more good reason why London lures the brightest and best. Within a few years of the big bang, London was fixed in the world's imagination as a place of opportunity, where the elite can pick up eye-popping bonuses or seven-figure salaries that can't be matched outside New York. "This is the only place in Europe where you can make a 1 million pounds a year while working for someone else," says Tony Travers of the London School of Economics. Add tax rates that are indulgent by some West European standards--and it's easy to see why the high-fliers would opt for London over Paris.

Regulation "lite" carries over to other spheres, from the arts or entertainment. Not by coincidence, London is a center for both. Ask Jorg Roth, a German TV producer who moved to London in 1999 to start his own production and distribution company. "You can lay people off with only seven days' notice in London when it takes three months in Germany," says Roth, who employs a staff of 15 with freelancers from all over the world. "I couldn't have done in Germany what I've done here in the last five years."

Language clinches London's pre-eminence. Many newcomers choose the city because they can use (or learn) English. A quarter of the world's population is now fluent or at least competent in the language, and even a shaky command opens up one level of the London job market. The city's middle classes have come to depend on a ready supply of Australian barmen, Hungarian nannies, Polish builders and Nigerian minicab drivers, not to mention the Ukrainians or Romanians who clean their offices--or quickly rise to employ those who do.

Can it last? To be sure, popularity has its price. Livingstone concedes that daily life in his rainbow city can be "scratchy and difficult." London motorists know to stay away from Trafalgar Square and other chokepoints where traffic regularly slows to a Dickensian horse-and-carriage crawl. Commuters endure daily frustration on a subway system starved of investment for decades, and where key stretches of line are prone to shut down with little notice. Violent crime is on the rise, the public-health system is chronically overloaded and the middle classes shun the low-grade public schools. A rising number of exasperated families are choosing to flee the city altogether.

And then there's the cost. Mercer Consulting last year ranked London as the world's most expensive city after Tokyo, a jump of five places over its 2003 ranking. The 2.50 pound price of a pint of bitter in some London pubs would shock a Czech beer swiller; the 2 pound charge for the shortest ride on the London Underground would appall a Parisian. Even the hardiest immigrants will take only so much discomfort. "I think people should go to Birmingham or Manchester," says 22-year-old Michael, a former political-science student newly arrived from Cracow, who's now earning just 3 pounds an hour--below the official minimum wage--delivering papers.

What's emerging, say the critics, is a divided London with almost 19th-century extremes of wealth and poverty. "This may be the capital of the world's fourth-largest economy, with thousands of homes worth more than a million pounds, but it has some of the nation's greatest housing inequality," says Adam Sampson of the housing charity Shelter, speaking at a riverside property fair in East London. "Go just inland and you'll find three generations of a single family crammed into a two-bedroom flat."

Maintaining the city's allure may therefore take more than the old hands-off approach. Indeed, after years of squabbling with the mayor, a worried national government has now lent its weight to the drive to build new homes and to restore the transport system. A 10 billion pound overhaul for the network is planned. Already, a congestion charge on motorists has eased the worst of the traffic problems in the inner city. Police numbers have risen steadily. Perhaps the biggest challenges of all involves resisting political pressures that might kill the golden goose--over-harsh anti-immigration policies, to name but one, that would diminish London's standing as Europe's only world city.