Mr Johnson's ousting of Ken Livingstone was the final act in a disastrous set of local elections for Labour, which have left Prime Minister Gordon Brown in a battle to reassert his authority. Click for ward-by-ward results »

Home Secretary Jacqui Smith said voters had delivered "a kick up the backside" to the Government, while minister for London Tessa Jowell described the results as "a pretty tough yellow card" for Labour.

Mr Brown will submit himself to a grilling in a pair of Sunday TV interviews in a bid to assure voters that he has understood the message of the elections, which saw Labour slump to its worst result in 40 years.

He was today urged to show he was listening to backbench concerns by dropping his proposals for 42-day pre-charge detention for terror suspects.

Labour MP David Winnick, leader of a successful rebellion against 90-day detention in 2005, warned that the "divisive" issue risked inflicting further damage on the party's position unless Mr Brown backs down before it reaches its final Commons stages in June.

Justice Secretary Jack Straw insisted that the 24% share of the vote achieved by Labour in Thursday's polls did not condemn it to defeat in a General Election, which he appeared to accept would not now be called until 2010.

"The situation in two years' time will be different from where we are today," Mr Straw told BBC Radio 4's Today programme.

"When you come to a General Election what people are doing is applying themselves directly to who should form the next Government and I think the choices will be very different from what has unquestionably been partly a protest vote in the mid-term."

Mr Straw said that voters had wanted to "punish" Mr Brown - before hurriedly correcting himself to say "punish us" - for the scrapping of the 10p tax rate. He warned that the Government must make "fewer mistakes", while stressing that it should not allow itself to be blown off course.

Mr Johnson's victory was being seen by Conservatives as a springboard for the May 22 Crewe & Nantwich by-election and the upcoming General Election, providing an opportunity to show voters a Tory administration in action.

But the new Mayor adopted a conciliatory tone in a speech today at City Hall, promising to build on Mr Livingstone's "considerable achievements" and urging Londoners of all political stripes to set aside personal rancour and ideological disputes to create "a London that is greater still".

Although he joked that he would "humanely euthanase" anyone who begrudged the change of power at City Hall, he took pains to stress that his would not be a partisan administration.

"It is vital for a Mayor of London to bring people together and to unite London and to serve every community in London impartially and to make sure we have in my administration representatives of all communities, which is what we will have," he said.

Details of his key advisors are due to be announced over the coming days.

Mr Johnson signed the declaration of acceptance of his new office just hours after the fatal stabbing of a 15-year-old boy in a south London block of flats, which brought the toll of teenagers murdered in the capital this year to 12.

Describing the boy's death as "tragic", Mr Johnson said: "I think this problem of kids growing up without boundaries and getting lost in tragic and self-destructive choices is the number one issue we face in this city.

"It is the job of me as Mayor to lead the fightback against it and that is what I want to do and I hope you will all join me in doing it."

He also pledged to make good on campaign promises to build affordable homes, protect gardens against development, improve bus services and "reform and improve" the congestion charge.

And he promised a clampdown on disorder on buses and trains, which he said was the single policy which most clearly resonated with the public during his election campaign.

"We are going to double the size of the safer transport teams to get people the sense of safety and security on the buses that they deserve," he said.

"I think there is a vital necessity to drive out so-called minor crime and disorder as a way of driving out more serious crime."

As Mr Livingstone visited City Hall to clear his desk, Mr Johnson went straight to work in a private meeting with commissioners for the capital's transport, police and fire brigade, though the seals of office are not formally handed over until midnight tomorrow.

"Until that time, I imagine there are shredding machines quietly puffing and panting away in various parts of the building, and quite right too," quipped the new Mayor.

"Heaven knows what we shall uncover in the course of the next few days."

True to his bumbling image, Mr Johnson was rarely far from a pratfall during the signing ceremony, several times raising laughter from his audience.

He had to ask what the date was before signing the acceptance document, muddled up the name of the architect responsible for City Hall's distinctive design and stumbled as he stepped up to make his speech. The podium on which he tripped was a "last-minute booby trap" on his road to power, he joked.

Labour backbencher Graham Stringer said ministers were privately discussing whether there should be a challenge to Mr Brown's leadership.

The Manchester Blackley MP told Sky News: "I think Gordon is going to be the leader of the Labour Party. There is no real tradition of regicide.

"But it would not be true to say that these conversations aren't going on between ministers and Labour backbenchers about whether there should be a challenge. Those conversations are being had.

"There is a public display of loyalty and there is private despair."

Left-wing Labour MP Jeremy Corbyn said that the party did not necessarily need a new leader, but should stop "aping the Tories" and return to its traditional values.

The Islington North MP told Sky News: "I don't think it's about, necessarily, the personalities or a challenge to Gordon.

"I think what party members and party supporters and MPs particularly want to see is some clear statements of policy that don't look as though we are aping the free market and the Tories but are standing up for the values that the Labour Party was founded for and has survived because of."

Mr Brown's decision to scrap the 10p tax rate, which hit the low-paid workers who make up much of Labour's core support, was neither "politically a very sensible thing to do or morally a very correct thing to do", he said.

Labour backbencher Graham Stringer said ministers were privately discussing whether there should be a challenge to Mr Brown's leadership.

The Manchester Blackley MP told Sky News: "I think Gordon is going to be the leader of the Labour Party. There is no real tradition of regicide.

"But it would not be true to say that these conversations aren't going on between ministers and Labour backbenchers about whether there should be a challenge. Those conversations are being had.

"There is a public display of loyalty and there is private despair."

Influential backbencher Jon Cruddas, who mounted a widely-admired challenge for Labour's deputy leadership last year, said it was not too late for the party to win the General Election, but warned it would have to change to do so.

He accused the party's leadership of taking the working class for granted as they tried to woo middle-class swing voters, and said that millions of traditional Labour voters had abandoned them as a result.

In an apparent dig at Mr Brown and senior Cabinet ministers' public response to the ballot-box drubbing, Mr Cruddas said it would not be enough for Labour simply to promise to "listen and learn".

In an article for tomorrow's Sunday Mirror, the Dagenham MP wrote: "Over the last few years, Labour has been losing elections because millions of our core supporters have decided to stay home on election days.

"Well, the missing millions are back - but now they're voting for the other side."

And he warned: "The bad news for Labour is that if we carry on as we are, it will carry on getting worse...

"Let's not mess about - our people are abandoning us, we're sinking fast, and no amount of hand-wringing and promises of `listening and learning' from election night will change that."

Mr Cruddas added: "We have to govern for everyone. That's why we need to remember those forgotten millions.

"Working class voters have been let down and patronised by a Government that was elected to represent them. As times get harder and the cost of living continues to rise the middle classes are also struggling. They need to feel that Labour understands their fears.

"We can speak with one voice. We don't need to play one half of Britain off against another. It's not too late to change - but choose change we must."

Prominent Labour left-winger John McDonnell this evening denied that he was planning a "stalking horse" challenge to Mr Brown's position as leader, with the goal of clearing the way for a more mainstream replacement to come forward.

The Hayes and Harlington MP tried to launch a bid for the leadership after Tony Blair stood down last year, but failed to secure the necessary 45 signatures of Labour MPs to get his name onto the ballot paper.

Mr McDonnell, who chairs the Socialist Campaign Group of left-leaning MPs, told PA: "I think we should have a leadership election. I think we should have had one last year, and the fact that we didn't is part of the reason why we are in this mess now, because we never had the chance to debate the issues.

"But I am certainly not mounting any stalking horse challenge. If I was going to run, I would do it seriously.

"I would welcome a leadership challenge at any time and I would welcome a wide range of candidates because I want a debate about issues, but it is not feasible. I couldn't get my name on the ballot paper last year, and for a challenge to an incumbent leader I would need 70-plus signatures."