Theresa May promises 'a country not for the privileged few, but for every one of us' as she becomes country's second female Prime Minister

Mrs May will take up office as Britain's second female PM on Wednesday, after Mr Cameron answers MPs' questions in the House of Commons for the last time and goes to Buckingham Palace to offer his resignation to the Queen.

Even before arriving at 10 Downing Street, Mrs May was facing calls for a snap general election from Labour, who said it was "crucial" that the UK has a "democratically elected Prime Minister" at a time of economic and political instability following the vote to leave the EU.

David Cameron speaks in Downing Street yesterday

The Home Secretary was unexpectedly transformed from leadership candidate to prime minister-designate by the sensational decision of her only rival, Andrea Leadsom, to pull out of the race to succeed Mr Cameron, which had been due to last until September 9.

Admitting she was "shattered" by a torrid few days of negative headlines since securing her place on the ballot paper for a nationwide poll of Tory members, Mrs Leadsom conceded she had too little support among MPs to offer "strong and stable government", and offered Mrs May her "full support".

Mrs May - who rushed back to Westminster from a campaign speech in Birmingham - appeared outside Parliament to declare herself "honoured and humbled" to become the Conservative leader.

Accompanied by husband Philip and flanked by dozens of applauding MPs from all sides of the party, Mrs May said she would offer "strong, proven leadership to steer us through what will be difficult and uncertain economic and political times".

She repeated her message that "Brexit means Brexit", in a clear bid to reassure Eurosceptic Tories that she will make good on the referendum vote to quit the EU, despite being a Remain supporter during the campaign.

And she set out her One Nation vision of "a country that works not for the privileged few, but that works for every one of us", adding: "We are going to give people more control over their lives and that's how together we will build a better Britain."

Theresa May outside the Houses of Parliament in Westminster, London, after she secured her place as the UK's second female prime minister​

Her speech in Birmingham signalled a sharp change in direction for the Government when she takes the helm, promising "a different kind of Conservatism" that will "get tough on irresponsible behaviour in big business" and give ordinary workers a greater share in economic growth.

In comments indicating she recognises voter "frustration" with the austerity offered by Mr Cameron, she said the June 23 referendum was not only a vote to leave the EU but also "a vote for serious change".

She set out a series of plans to rein in executive pay and bonuses, put workers into the boardroom and tackle market abuses by banks and utility companies, while also putting multinational companies such as Amazon, Google and Starbucks on notice that she expects them to pay their taxes in full.

Mr Cameron said he was "delighted" that the 59-year-old Home Secretary will replace him in Downing Street.

Speaking outside Number 10, he said: "She is strong, she is competent, she is more than able to provide the leadership that our country is going to need in the years ahead and she will have my full support."

Andrea Leadsom makes her statement yesterday morning

Mrs May also won the backing of Brexit standard-bearers Boris Johnson and Michael Gove, who issued messages of support immediately after Mrs Leadsom's withdrawal, at a time when there was still some confusion in Westminster over whether she would now have to fight a different opponent.

Mr Johnson said he had "no doubt Theresa will make an excellent party leader and Prime Minister", while Mr Gove - who was eliminated from the leadership contest after taking third place in last week's vote by MPs - said Mrs May had "my full support as our next Prime Minister".

Labour election co-ordinator Jon Trickett said he was putting the whole party on general election footing, on the very day when its own leadership contest was kicked off by a formal challenge to Jeremy Corbyn from Angela Eagle.

Mrs May set her face against a snap election when she launched her campaign for the Tory leadership on June 30, saying: "There should be no general election until 2020."

But other parties are likely to remind her of Mr Cameron's demand for an immediate election in 2007, on the grounds that Tony Blair's successor Gordon Brown "doesn't have the mandate (and) wasn't elected as prime minister".

Mr Trickett said: "It is crucial, given the instability caused by the Brexit vote, that the country has a democratically elected Prime Minister. I am now putting the whole of the party on a general election footing. It is time for the Labour Party to unite and ensure the millions of people in the country left behind by the Tories' failed economic policies have the opportunity to elect a Labour government."

Liberal Democrat leader Tim Farron demanded an early election, saying: "The Tories now have no mandate. Britain deserves better than this."

And Green MP Caroline Lucas - herself a candidate for her own party's leadership - said it was "unacceptable" that the next PM should be appointed only by Conservative MPs rather than chosen by voters.

Plaid Cymru's Westminster leader Hywel Williams said he anticipated many disagreements with Mrs May in the coming months, but said he wished her well as she led the negotiations on Britain's disengagement from the EU.

He said: "First and foremost, the UK needs certainty. Wales, more than any other country in the UK, relies on its trading relationship with the European Union and I will be seeking urgent assurances from Theresa May that the UK Government will not allow a vote to leave the EU to lead us towards leaving the European single market."