In Los Angeles, which some Londoners still like to deride as a la-la land, the London mayoral election was described as loony versus loonier. Its winner must now prove Californians, and much of the rest of the world, wrong. London's status as a global city depends critically on perceptions, which no one has more power to shape than its mayor. So Boris Johnson must show that he is as serious about governing as he turned out to be about campaigning. He must confound those in the capital and its assembly who remain deeply worried because, until this morning, he had not been directly responsible for anything bigger than a conservative magazine or the Henley constituency. He must bring in his team without paralysing the rest of City Hall.

Mr Johnson has already promised a brisk start. His speech on accepting office was unscripted even by his standards, but briefings afterwards were intended to send clear signals that he will follow up his campaign promise of a crackdown on petty crime with the swift deployment of 440 new police community support officers; and that he will cut back the mayor's own personal bureaucracy to help to finance this initiative.

So far, so good - but with Mr Johnson, more than most, the gap between talk and action remains unbridged. No one doubts the quality of his intellect. A respectable majority of Londoners have shelved what doubts they had about his seriousness. Yet few pretend that he has much genuine appetite for detail or first-hand expertise in tackling crime, public transport or economic development. His overwhelming priority, therefore, is to appoint the right people to deliver on his promises in these areas, and to do it fast.

Skilful delegation to deputy mayors with clearly defined responsibilities should allow Mr Johnson to act as chairman rather than chief executive. This will be vital if he is to chair the Metropolitan Police Authority, as he wishes, without spreading himself too thin. But no amount of delegation will absolve him of decision-making on weightier issues than he is used to.

On crime, he has made no secret of his dissatisfaction with Sir Ian Blair as Metropolitan Police Commissioner, and has indicated at the weekend that he will push for Sir Ian to go if his performance does not improve. He must urgently clarify how he intends to measure that performance, and forge a sensible working relationship with the Met in the meantime. On transport, Mr Johnson can slay his bête noire, the bendy bus, and he should do so. They are fundamentally incompatible with London. His preferred alternative, an updated Routemaster, looks likely to cost ten times the initial estimate to develop, and he has not made clear how conductors would be paid for.

On London's economy, which drives the nation's, Mr Johnson has allowed himself to be labelled the friend of small business but the second choice of the City. He must be an unstinting ally of both. That may entail breaking with his party on the tax status of non-domiciled millionaires, whose exodus is already taking the shine off London's hubristic claim to be “capital of the world”. It will also entail tirelessly emphasising that London welcomes foreigners of all wealth brackets, not just the richest 1 per cent. Their striving, and their spending, helps to define the capital.

Mr Johnson said that he entered politics because no one ever put up a statue of a journalist. There will be no statue of him as mayor, either, if he fails to deliver. His powers and budget are limited. His influence is not. He must use it wisely.