Will new leader Theresa May keep Britain on course for Brexit?

How will Theresa May handle Brexit?

LONDON -- Number 10 Downing Street in London is the official residence of the British Prime Minister; the house where most important government business is conducted. Very soon, reports CBS News correspondent Elizabeth Palmer, there will be moving vans at the door.

Theresa May saluted cameras as she arrived at the prestigious address Tuesday morning for a meeting. Soon she'll move in -- both to the house, and to Britain's top job, taking over from Prime Minister David Cameron.

Cameron said immediately after Britain voted to "Brexit" the European Union that he would step down to make way for a new national leader.

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But it has all come about even more quickly than anticipated, with Cameron telling lawmakers on Monday, that, "on Wednesday, I will attend the House of Commons for Prime Minister's Questions. And then after that I expect to go to the palace and offer my resignation, so we will have a new prime minister in that building behind me by Wednesday evening. Thank you very much."

That soon-to-be prime minister was surrounded by Conservative Parliamentarians as she accepted the post, saying she was "honoured and humbled to have been chosen."

Her biggest challenge by far will be managing Britain's departure from the European Union.

She didn't support the movement to see the U.K. pull out of the world's largest free trade bloc, but she has vowed to respect the will of the people expressed in the landmark referendum, assuring the nation that "Brexit means Brexit."

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But does it? May herself voted against Brexit in the referendum, and there's speculation she may try to negotiate a compromise with the EU. Whatever her strategy, May's colleagues agree she'll be a steely negotiator.

For the past six years she's been Britain's Home Secretary, in charge of policing, immigration and counterterrorism. She's earned herself a reputation as a tough legislator -- not charismatic, necessarily -- but disciplined and good on detail.

Her sudden rise to the leadership has inevitably recalled Britain's last female Prime Minister, Margaret Thatcher, who left office in 1990, 26 years ago.

May will lock horns with Europe's other powerful female head of state, German Chancellor Angela Merkel, who wants the U.K. to begin negotiating its way out of Europe pronto.

May, however, has already said she won't even begin the process until 2017.