Live: Prime Minister Theresa May names Philip Hammond as Chancellor, George Osborne resigns

Prime Minister Theresa May has taken office as the UK’s second female Prime Minister with the promise to create “a country that works for everyone.”

Speaking outside the famous black door of 10 Downing Street, Mrs May said that the decisions of her administration would be driven not by the interests of “the privileged few” but those of voters struggling with the pressures of modern life.

Just minutes after being invited by the Queen to form a Government, the new Prime Minister stressed her determination to preserve the Union between England, Scotland, Wales and Northern Ireland. And she promised she would “rise to the challenge” of negotiating exit from the European Union and forge a “bold new positive role” for Britain in the world.

But her strongest message was of her intention to serve as a “One Nation” Conservative PM acting on behalf of all voters, not just the Tories’ traditional supporters in the comfortable suburbs and shires, and the world of business.

In a direct message to voters, she said: “I know you are working around the clock, I know you are doing your best and I know that sometimes life can be a struggle.

“The Government I lead will be driven not by the interests of the privileged few but by yours. We will do everything we can to give you more control over your lives.”

Mrs May’s elevation to the country’s most senior political role, at the age of 59, completes a whirlwind rise which was triggered by the unexpected referendum vote for Brexit on June 23 which brought down predecessor David Cameron.

She “kissed hands” with the monarch in a simple procedure at Buckingham Palace which made her the 13th holder of the post of Prime Minister and First Lord of the Treasury during Elizabeth II’s reign.

Mrs May arrived at the Palace by ministerial car with husband Philip, having set off from the House of Commons only after receiving the signal that predecessor David Cameron’s resignation as PM had been accepted by the Queen and that he had advised the head of state to appoint the former Home Secretary in his place.

Mr Cameron was accompanied by wife Samantha and children Nancy, Elwen and Florence as he left 10 Downing Street for the last time as Prime Minister.

Standing with his family outside the famous black door, Mr Cameron said that he believed he was leaving the country “much stronger” and the economy “immeasurably stronger” after his six years in office.

In a clear bid to define the legacy that he will leave behind him, he spoke of his pride at achievements including reducing the deficit, legalising gay marriage, boosting employment, introducing the National Living Wage, increasing international aid spending and cutting waits for NHS treatment

And he paid tribute to Samantha, who he described as “the love of my life” who had “kept me vaguely sane”.

Mr Cameron said he was “delighted that for the second time in British history the new Prime Minister will be a woman, and once again a Conservative”.

And he said Mrs May would provide “strong and stable leadership in delivering the Conservative manifesto on which we were elected” and wished her well in negotiating “the best possible terms for Britain’s exit from the European Union”.

Mr Cameron concluded: “It has been the greatest honour of my life to serve our country as Prime Minister over these last six years and to serve as leader of my party over 11 years.

“And as we leave for the last time, my only wish is continued success for this great country that I love so very much.”

After being forced out of the premiership by last month’s referendum vote to quit the EU, Mr Cameron won a standing ovation from Conservative MPs and applause from some of the opposition as he ended his last session of Prime Minister’s Questions in the House of Commons by telling them: “I was the future once.”

Urged by veteran Tory Kenneth Clarke to remain an “active participant” as the House copes with the fallout from Brexit, Mr Cameron said: “I will watch these exchanges from the back benches. I will miss the roar of the crowd, I will miss the barbs from the opposition, but I will be willing you on.”

Speaking of his pride at presiding over record employment, improved school standards, the introduction of gay marriage and lifting low-paid people out of income tax, Mr Cameron told MPs: “You can achieve a lot of things in politics ... In the end, public service, the national interest, that’s what it’s all about.”

Watched from the public gallery by wife Samantha and children Nancy, Elwen and Florence, Mr Cameron paid tribute to the support he had received from his family, telling MPs: “The pressure often bears hardest on those around us in this job.”

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And in response to the news that the family are leaving the Downing Street cat behind at Number 10, he assured MPs: “I love Larry.”

Listing his engagements for the day, Mr Cameron joked that “other than one meeting this afternoon with Her Majesty the Queen, my diary for the rest of the day is remarkably light”.

Ulster Unionist MP Danny Kinahan paid tribute to Mr Cameron’s “hard work and leadership” and suggested that he might be interested in taking up positions which had become available as manager of the England football team, presenter of BBC One’s Top Gear or president of the United States.

Labour leader Jeremy Corbyn suggested the PM could take up Len Goodman’s job on TV’s Strictly Come Dancing - though the PM admitted “I don’t really have a pasa doble”.

Despite devoting the bulk of his six questions to housing and Europe, Mr Corbyn paid tribute to Mr Cameron’s achievement in legalising gay marriage and securing the release of British resident Shaker Aamer from Guantanamo Bay and wished him and his family well as he leaves office - as well as asking him to thank his mother for her advice about his suits and ties.

Mr Cameron thanked the Labour leader for his comments, but also took a string of pot-shots at the opposition, saying: “When it comes to woman prime ministers, pretty soon I am pleased to say it is going to be two-nil - and not a pink bus in sight.”

The outgoing PM is later expected to make a statement in Downing Street setting out what he sees as his legacy, before going to Buckingham Palace to offer his resignation to the Queen.

Mrs May will follow him to the Palace to be formally appointed his successor by “kissing hands” with the head of state, and is expected to make her first speech as PM outside the famous black door to Number 10, outlining her priorities for the new administration.

Britain’s new prime minister will swiftly begin drawing up her new top team and is expected to increase the number of women in government.

She will make appointing a cabinet minister to take charge of Brexit one of her first tasks as she enters No 10 as Britain’s second female PM.

Although a Remain supporter, Mrs May has repeatedly stressed that “Brexit means Brexit” and the hunt for a building to house the department that will steer Britain out of the European Union is already under way.

After presenting herself as the unity candidate, the incoming leader is expected to offer plum posts to leading figures from both camps in the EU referendum.

George Osborne looks unlikely to stay on as Chancellor after the PM-to-be trashed parts of his economic legacy in a campaign speech on Monday, with Philip Hammond, who has long coveted the role at the Treasury, among those who could take over.

Senior Brexiteer Chris Grayling will be rewarded for his role running Mrs May’s campaign.

Andrea Leadsom, whose shock withdrawal from the leadership race meant the expected nine-week leadership campaign was truncated to just a couple of days, is expected to be offered a job in recognition of her raised profile.

Big question marks are hanging over the future of Brexit standard-bearers Boris Johnson and Michael Gove, who were seen to have blotted their copy-books in the wake of the referendum result.

Mrs May, a founder of the Women2Win group to increase the number of female MPs, is keen to see more women in “prominent” roles.

A spokeswoman for Mrs May said: “Civil servants have already been charged with finding a building to house the Brexit department - an indication of Theresa’s commitment to get on with delivering the verdict of the EU referendum. Brexit means Brexit and we’re going to make a success of it.”

They added: “It was Theresa that set up the campaign to elect more female MPs to parliament - and she has always believed that there should be more women in prominent government positions.”