“Under my leadership the Conservative Party will come back together in the interests of the whole country”, she added.
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SEE MORE: Theresa May Could Be The UK’s Next Leader; So, Who Is She Again?
May received 199 votes in a ballot of Conservative members of Parliament, while Leadsom received 84.
British Justice Secretary Michael Gove was eliminated from the Conservative leadership race with 46 votes.
The Conservative Party’s 150,000 members will now decide the victor of the final run-off, with the new leader due to be announced on September 9.
But he welcomed the fact that the next Prime Minister would be a woman.
The result is expected to be announced on September 9.
Reuters spoke to five former Invesco colleagues, including four in senior management positions, who said Leadsom did not have a prominent role or manage client money.
May was appointed Home Secretary in 2010, after the Conservative Party took control of the government.
Former UKIP leader Nigel Farage, one of the chief proponents of Brexit, and London Mayor Boris Johnson both have endorsed Leadsom. She also serves as the home secretary.
Under contest rules, Gove is now eliminated, while May and Leadsom will face one another in a vote of the 150,000 party members.
Mrs May (59) was a “Remain” supporter but kept a relatively low profile during the European Union referendum campaign.
The victor will become the country’s second female prime minister following Margaret Thatcher, who held office from 1979 to 1990.
After winning the most votes from parliamentary colleagues, Mrs May said the United Kingdom needs “strong, proven” leadership to handle Brexit negotiations and unite the country.
Ms Davidson, who got engaged to her long-term partner Jen Wilson in May, said she would invite the next prime minister to her marriage – even if it was Mrs Leadsom, who has expressed concerns about same-sex weddings.
“The decision we took on June 23 was a great moment in history”, she said at her campaign launch in July.
May, who campaigned to remain in the European Union, received an endorsement from The Sun newspaper that said on its front page the “new Mrs T must be Tezza not Leadsom”. Mr Johnson got his own revenge by throwing his support behind Mrs Leadsom.
Gove said he was “naturally disappointed” to be out of the race, but said “both Theresa May and Andrea Leadsom are formidable politicians”.
Ms May was on Team Remain, but says she’ll ensure the Brexit means all boats will rise and “make Britain a country not for the privileged few, but for everyone”.
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One of the MPs who is backing Mrs May, Defence Secretary Michael Fallon, told Sky News: “I think at a time like this you need somebody with the experience and the track record to help stabilise the economy, to deal with threats from overseas and to reassure our allies”.
