THERESA May has been appointed the UK's second female Prime Minister in a private audience with the Queen at which she was invited to form a Government.

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.

Speaking before she entered 10 Downing Street for the first time as PM, she said: ''I have just been to Buckingham Palace where Her Majesty the Queen has asked me to form a new Government and I accepted.

''In David Cameron I follow in the footsteps of a great modern Prime Minister.

''Under David's leadership the Government stabilised the economy, reduced the budget deficit and helped more people into work than ever before.

''But David's true legacy is not about the economy but about social justice.

''From the introduction of same sex marriage to taking people on low wages out of income tax altogether, David Cameron has led a One Nation government and it is in that spirit that I also plan to lead."

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.''

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.''