Speaking at a press conference, May announced her candidacy for leadership, saying she was the woman for the job of leading the U.K. amid a period of uncertainty following the Brexit vote.
"Following last week's referendum, our country needs strong clear leadership to steer us through the uncertainty following the Brexit vote," she said, adding that the next leadership needed to unite the Conservative party and the country. "We need a bold new positive vision of the party that works for everyone in the country, not just the privileged few."
Thursday marks the deadline for politicians to enter their bids for the leadership race. Prime Minister David Cameron resigned after the U.K.'s referendum on EU membership delivered a Brexit vote despite his efforts to persuade voters to stay in a reformed EU. Like other candidates, May rules out a second referendum and said that "Brexit means Brexit." She also ruled out a general election until 2020.
Also launching his bid on Thursday morning, Brexit campaigner Michael Gove detailed why he had chosen to run for the leadership, rather than supporting Boris Johnson, with whom he campaigned.
"I respect and admire all the candidates running for the leadership. In particular, I wanted to help build a team behind Boris Johnson so that a politician who argued for leaving the EU could lead us to a better future. But I have come, reluctantly, to the conclusion that Boris cannot provide the leadership or build the team for the task ahead. I have, therefore, decided to put my name forward for the leadership," he said in a statement.
While 52 percent of Brits voted to leave the EU, the remainder is generally unhappy at the prospect of leaving the economic and political bloc, fearing a loss of jobs, trade, growth and openness to the wider world.
Sir Nigel Sheinwald, former British Ambassador to the U.S. told CNBC that the U.K.'s political scene was "pretty unstable" at the moment.
"It's very unclear day-by-day the way things are going to go or the way that the choices that are made about who leads our parties and who's in the most senior positions will affect policy on issues and interests which are long-lasting and will go well-beyond the term in office of the people we're talking about."
Still, the U.K. has yet to initiate any withdrawal process from the EU with Cameron insisting that Article 50 of the Lisbon Treaty, which kickstarts the exit, will not be invoked until a new Conservative party leader is in place – expected to be around September – much to the consternation of his EU counterparts who want no further delay following the vote to leave.
Daniel Hannan, a member of the European parliament for the U.K.'s Conservative Party who was prominent in the campaign to leave the EU, told CNBC that the Brexit vote did not entail Britain closing its borders.
"No one is talking about closing our borders. What Theresa said (in her leadership bid) and what people have said throughout the (leave) campaign is that we want more control but that doesn't mean that we're going to raise the drawbridge," he said, commenting after Gove and May's bids were announced.
"We're very much open for business and one of the main reasons why we - those of us that did - campaigned to leave the EU is because we want freer trade with the U.S., Australia, India, China and the bits of the world that are actually growing."
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