Her policy moves as home secretary have included reducing the minimum wage of non-EU workers wanting to work in the UK.
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Prime Minister David Cameron said he would step down by October.
Ms Leadsom came second in Thursday’s Tory leadership vote, garnering the support of 84 MPs, but lagged significantly behind the Home Secretary Ms May who won 199 votes.
Though he did not immediately announce his backing for either May or Leadsom, he said that he welcomes the fact that the United Kingdom will have its second female prime minister, and called for a “civilised, inclusive, positive and optimistic debate”.
The 59-year-old May, who supported the losing “remain” side, said she is the best person to unite a party that, like the country, is divided over the referendum result.
“This vote shows the Conservative Party can come together and that under my leadership it will”.
Pro-EU Mrs May and pro-Brexit Mrs Leadsom will now go head-to-head in a ballot of around 125,000 Conservative members across the country in the next few weeks.
If elected, May would be tasked with the hard job of negotiating the U.K.’s exit from the EU.
Thatcher, who served as Britain’s leader from 1979 to 1990, was the country’s first and only female PM.
Leadsom, 53, who backed the “leave” campaign in the referendum, entered Parliament in 2010 after a career in financial services. Cameron had campaigned to remain.
“I’ve won votes from Conservatives MPs across the party – from left and right, from Leavers and Remainers, MPs from the length and breadth of the country”.
Mr Gove said: ‘I’m naturally disappointed that I haven’t been able to make it through to the final round of this leadership contest’.
Mrs Leadsom played a high-profile role in the campaign for Britain to quit the EU.
“I think Andrea Leadsom would do a great job because she understands the positive advantages of leaving the European Union and how you can turn that to a great opportunity for our country”.
The pro-Brexit Ms Leadsom has attracted support from a series of leading figures in Ukip since announcing her candidacy, including the party’s major donor Arron Banks.
Mr Marr said some people claim Mr Farage is the “great victor of this [Brexit], in many respects, he should be there [ in the Brexit negotiations] and not pushed by the Westminster establishment”.
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“She has the experience, she is already a member of the National Security Council, she works to protect homeland security just as I deal with threats overseas like Daesh (Islamic State) and our commitments to North Atlantic Treaty Organisation and we work together”.
