May backed the "Remain" camp during the campaign for Britain's referendum on EU membership on June 23 but has made clear since then that it must now go ahead, saying: "Brexit means Brexit."
But she has also said Britain should not trigger the exit proceedings until London is ready to start negotiations.
Invoking Article 50 of the EU's Lisbon Treaty would begin those talks but lawyers and politicians differ over who has the authority to trigger the clause and whether it is irreversible.
"There should be no decision to invoke Article 50 until the British negotiating strategy is agreed and clear -- which means Article 50 should not be invoked before the end of this year," May (59) said late last month when she launched her campaign to succeed Prime Minister David Cameron.
That potentially puts May on a collision course with German Chancellor Angela Merkel, who is often portrayed as the EU's most influential politician as leader of its strongest economy.
Merkel said on Monday talks with Britain would "not be easy" and has said she expects London to begin the formal process of leaving as soon as it picks a new prime minister.
May, whose only remaining rival quit the race to replace Cameron on Monday, will be Britain's first woman prime minister since Margaret Thatcher, who governed from 1979 until 1990.
Cameron, who called the vote to appease anti-EU lawmakers in his own party but campaigned for continued membership, said he plans to tender his resignation to Queen Elizabeth on Wednesday. May will take office the same day.
'Difficult'
Article 50 envisages a period of up to two years to negotiate an amicable separation.
Triggering it quickly might weaken London's hand in negotiations on the terms of its break with the EU but any delay could add to uncertainty for investors wondering how the future relationship with the EU will look.
Supporters say she has steely determination, pays attention to detail and focuses on getting on with the job at hand. She has also been described by a Conservative Party grandee, Ken Clarke, as a "bloody difficult woman".
May has made clear she will respect the will of the British people, expressed in the referendum last month.
"There will be no attempts to remain inside the EU, no attempts to rejoin it by the back door, and no second referendum. The country voted to leave the European Union and as Prime Minister I will make sure that we leave the European Union," she said during a speech on Monday.
May has said she plans to appoint a minister for Brexit and that a priority will be to win the right for British companies to trade with the EU's single market in goods and services after it leaves the bloc, though freedom of movement will have to be curbed.
"The Brexit vote was also a message that we need to bring control to free movement. Free movement cannot continue as it has up to now," she said on Monday.
Merkel has said there can be no "cherry picking" of what it wants to keep from its EU membership while jettisoning aspects of the relationship that it does not like.
"We will have difficult negotiations with Britain, it will not be easy," Merkel told conservative supporters in eastern Germany on Monday.
The EU wants Britain to commit to leaving by early 2019 and has said there can be no negotiation before Article 50 is triggered. It has no clear legal power to hold Britain to an exit schedule but has some levers against disruptive members. .
'Stakhanovite'
May entered parliament in 1997 and became the Conservative Party's first female chairman in 2002, when it was not in power. She told its annual conference that year that people saw it as "the nasty party".
Colleagues say she shuns the old boys club traditions of parliament, preferring to spend any free time she has with her husband of 36 years, Philip.
"I know I'm not a showy politician," she said when she launched her leadership bid after Cameron said he was stepping down following the vote for Brexit.
"I don't tour the television studios. I don't gossip about people over lunch. I don't go drinking in parliament's bars. I don't often wear my heart on my sleeve. I just get on with the job in front of me."
May has Type One diabetes and needs insulin injections several times a day. She describes herself as a practising Christian and says she owns over 100 cookery books.
"She gets up very early. She does a bit of time in the gym to make sure she stays in shape because of course she needs to look after her health," said a Conservative lawmaker who has worked closely with her.
May, who has been Home Secretary, or interior minister, since 2010, has won plaudits from other party members while in the job. She has pushed through measures including reforms of the police and moves to tackle modern slavery.
"She was completely Stakhanovite in work ... she was very organised but also she had clear priorities. She had a very clear sense of long-term direction as well as the capacity to do the detail," Conservative lawmaker Damian Green told Reuters of his time working as a junior minister in her department.
He described her as a politician who "wasn't to be pushed aside or pushed about."
