The mayor looked on, bemused, as a member of the London Assembly informed him that she wholeheartedly backed his policy on cycle helmets.

Boris Johnson, who has vowed to protect his blond mop but has been caught riding without a helmet more than once, threw his hands skywards before remarking wryly: “How can you possibly agree? My position is hopelessly muddled.”

It is with such remarks that Mr Johnson has forged his political career, attracting a reputation as a bumbler and bungler, although often endearing himself to the public as a result.

However, the challenges of his first three months as mayor have arisen not from his own gaffes, as detractors had promised, but from those of the people around him. Early on Mr Johnson’s political strategist, James McGrath, quit after saying immigrants could leave if they did not like the administration.

The storm had barely settled when Ray Lewis, his most prominent appointee, was forced to deny claims of inappropriate conduct and financial irregularities during his time as a vicar. Initially Mr Johnson stood by him but accepted Mr Lewis’s resignation the following day when a government department refuted his claim to be a magistrate. The mayor’s team has since admitted that appointments were not properly vetted.

Last week Mr Johnson’s rocky relationship with Sir Ian Blair, the Metropolitan Police Commissioner, worsened when The Times obtained e-mails revealing that Kit Malthouse, another deputy mayor, wanted to suspend him. Mr Malthouse had to be informed by lawyers that the mayor had no such power.

A greater test has been the spate of fatal stabbings of teenagers on London’s streets. Mr Johnson is determined to tackle crime and claims his youth policy, including parenting classes and “respect” schools for disaffected youths, will work. More measures will be unveiled in the autumn.

He has banned alcohol on the Tube and announced additional uniformed officers on public transport to enhance safety. Hundreds of people have been arrested for knife-related offences.

Other policies include a Mayor’s Fund, formed from business donations, to help underprivileged communities, phasing out bendy buses, a skills exchange with New York, and “low-carbon zones” to cut emissions.

Political strategists warn that, while policies have come thick and fast, they lack a common thread. They say that Mr Johnson’s vision for London is still unclear and that he must work over the next 100 days to instil clarity.

In particular, environmental lobbyists are concerned that Mr Johnson scrapped Ken Livingstone’s £25 gas-guzzler charge and is reviewing the western extension of the congestion charging zone.

Mr Livingstone, for his part, is unimpressed, telling The Times that Mr Johnson had overseen the capital’s “slow collapse back into barbarism”.

Times Recommends

• Time-worn Freddie gives up Test matches
• Brighton company 'involved in cyber attack'
• The art of survival: it's all in the mind