WATCH: Theresa May outlines her vision for Brexit at Birmingham campaign launch

In a speech in Birmingham, Mrs May made clear her intention to reach out beyond the comfortable middle-classes who make up the traditional bedrock of Tory support, saying she wanted to create "a country that works not for the privileged few, but for every one of us".

The Home Secretary, who was a low-key supporter of Remain during last month's EU referendum, sought to reassure Eurosceptics that she will not attempt to overturn the result, repeating her declaration that "Brexit is Brexit".

And she drew a distinction with Andrea Leadsom by saying that her victory in the MPs' ballot at Westminster last week - when she took 199 votes against her opponent's 84 - made her the candidate able to unite all sides of the Conservative Party.

However in a shock revelation just moments later, Mrs Leadsom dropped out of the race, apparently clearing the way for Mrs May to become prime minister.

• MORE: Andrea Leadsom quits race leaving Theresa May as only candidate

Mrs May's speech came after Energy Minister Mrs Leadsom apologised to Mrs May by text "for any hurt I have caused" after she appeared to suggest in a newspaper interview that being a mother gave her an advantage over the childless Home Secretary as a potential prime minister.

Addressing supporters in Birmingham, Mrs May made a point of the fact that she had won the "overwhelming" support of Tory MPs in last week's election at Westminster, taking nearly two-thirds of votes including "left and right, Leavers and Remainers, MPs from the length and breadth of Britain".

"The results showed that, after the referendum, the Conservative Party can come together and under my leadership it will," she said.

And she set out the three key messages of her leadership campaign: "First, our country needs strong, proven leadership to steer us through this time of economic and political uncertainty and to negotiate the best deal for Britain as we leave the EU and forge a new role for ourselves in the world.

"Because Brexit means Brexit, and we're going to make a success of it.

"Second, we need to unite our party and our country.

"And third, we need a bold new positive vision for the future of our country - a vision of a country that works not for the privileged few, but for every one of us."

Asked about Mrs Leadsom's comments following her speech, Mrs May said: "I accept the apology and I am here today actually ensuring that what I am doing is talking about what I would want to do as prime minister and leader of the Conservative Party."

Mrs May insisted there will be "no attempts" to remain in the EU or to rejoin it "by the back door".

"As prime minister, I will make sure we leave the European Union," she said.

Mrs May said the Conservatives would be "completely, absolutely, unequivocally at the service of ordinary working people" under her leadership.

She pledged to create a democracy that "works for everyone so we can restore trust and confidence in our most important institutions".

The Home Secretary said that ordinary workers made "real sacrifices" after the financial crash and do not feel the economy works for them .

Wages have "grown but only slowly", taxes for the lowest paid went down but other levies such as VAT went up, energy bills "have rocketed", low interest rates and quantitative easing have helped homeowners "at the expense" of those who cannot get on the property ladder, she said.

Mrs May said there was a "growing divide" between a more prosperous older generation and "struggling" young people, as well as a "gaping chasm" between London and the rest of the country.

Many political and business leaders have responded to the EU referendum result "by showing they still don't get it".

She said: "I'm going to make sure that the motives of the government will never be in any doubt. We, the Conservatives, will put ourselves at the service of ordinary working people and we will make Britain a country that works for everyone whoever you are and wherever you are from."