LONDON — You can tell a lot about the differences between New York and London by comparing their mayors. Just as New York would never elect a socialist, let alone a corrupt one, so London would never elect a capitalist, even an honest one.

New York is proud to be represented by one of its wealthiest and most philanthropic citizens, Michael Bloomberg, whose fortune is founded on one of the world’s most innovative media companies and who does not even need to draw his salary. London’s Kenneth Livingstone cultivates his cockney accent and his image as a cheeky chappie, but his lavishing of public money on frauds and fanatics reveals him to be less a man of the people than an ideologue and a ruthless machine politician.

Yet cities change, sometimes even for the better. New York changed during Rudolph Giuliani’s time in City Hall as it reclaimed the streets and rediscovered its better self. Now London may be about to change, too: not just in its attitude to crime and punishment, but in the belated recognition that the British capital needs capitalism to thrive.

Next month, London will vote for a new mayor. Mr. Livingstone, the first and so far only holder of this office, has already enjoyed two terms. Indeed, he has enjoyed himself so much at Londoners’ expense that he is running again: unlike New York, which makes its own laws and wisely limits its mayors to two terms, London’s municipal constitution is framed by a statute which it has no power to alter.

Parliament ignored the obvious danger of giving the mayor unlimited tenure: if all power tends to corrupt, as Lord Acton said, then no power corrupts more absolutely than that of a mayor who clings to office to prevent his own misdeeds coming to light.

Nowhere was this phenomenon more obvious than in France under Jacques Chirac, who used his presidential powers to suppress allegations of corruption as the first modern mayor of Paris between 1977 and 1995. Only since he left office last year have the courts been permitted to investigate properly, and the chances of Mr. Chirac ever facing trial for his abuse of power over nearly two decades are slim.

Mr. Livingstone, too, has been dogged in his bid for reelection by accusations of corruption, which have forced his closest adviser, Lee Jasper, to resign mid-campaign. Few Londoners believe that Mr. Livingstone himself did not know what his associates were doing in his name, and the scandals have hurt him badly.

Eight years in office is a long time to make enemies. Mr. Livingstone’s policy of divide and rule has always depended on cultivating the idle, the parasitical and the unpatriotic elements while ignoring the hard-working, wealth-creating, law-abiding segment of the population. But the prosperity of the City of London has trickled down to untold millions, few of whom like to see their mayor hobnobbing with demagogues like Hugo Chavez, while the feminists and homosexuals who used to rally to Mr. Livingstone’s cause have been repelled by his espousal of Sheikh Qaradawi, the so-called “pope of Islam,” who would like to have them stoned to death.

The conservative rival to Mr. Livingstone is Boris Johnson, another figure who would be almost unimaginable as mayor of New York. Until the last few weeks, not many of Mr. Johnson’s conservative colleagues believed in his chances either. His improbability has nothing to do with his colorful private life — that never stopped Rudy Giuliani — but everything to do with a public persona that seems to be inspired less by Karl Rove than by P.G. Wodehouse. Boris — as he is affectionately known by a public that treats him as a comedian rather than a member of the loathed tribe of politicians — is a master of the misspoken arts who makes even Hillary Clinton look like an amateur. Having gratuitously insulted (and later apologized to) Liverpool and Portsmouth — two cities where he wasn’t even running for office — Boris was regarded as a high-risk candidate who might implode at any time.

Yet he has done nothing of the kind. He has fought a skilful campaign and is leading the opinion polls by up to 12 points. He has cast off his past as a buffoon and is now a figure with whom his party leader, David Cameron, is happy to be photographed.

What would Boris do as mayor? He promises to make the streets as safe as New York’s, though whether he is prepared to bully the officers of the Metropolitan Police into patrolling the streets, deterring crime rather than merely reacting to it, is doubtful. It would be a start if, instead of treating crime as inevitable, he inspired citizens to defend themselves and their neighbors — and made sure that the law did not penalize them for doing so.

The trickiest issue will be the 2012 London Olympics. One thing Mr. Johnson cannot shirk, if he is to be taken seriously: he must stop plans to build the biggest mosque in Europe, next to, and overshadowing, the Olympic village. This “mega-mosque,” which would dwarf even the largest cathedral, is driven by Saudi money and Tablighi Jamaat, an Islamist organization. It is opposed by moderate Muslims, including those it is supposed to serve, but it has been supported by Mayor Livingstone. So far, Mr. Johnson has kept stumm on the mega-mosque for fear of offending Muslim imams, who influence a lot of votes. Most Londoners hope he is only biding his time until after the election before putting a stop to what would be the most sinister and divisive building London had ever seen.