Theresa May is set to become Britain's next prime minister after Andrea Leadsom pulled out of the contest to become Conservative Party leader.
The timing of the hand over of power from British Prime Minister David Cameron is currently being discussed, BBC reported.
May, 59, who backed staying in the EU, has been home secretary since 2010.
Leadsom, who campaigned to leave the EU, said Britain needed a "strong and stable government" and that May was "ideally placed" to implement Brexit.
In a speech earlier on Monday setting out her leadership campaign platform, May -- who rejected the argument that the next leader and prime minister has to be someone on the winning side of the EU referendum -- said: "Brexit means Brexit and we're going to make a success of it."
Leadsom -- who was a leading light of the Brexit campaign -- said a nine-week leadership campaign at such a "critical time" for Britain would be "highly undesirable".
A source close to the energy minister told BBC "the abuse has been too great" for Leadsom during the contest.
Leadsom had apologised to May on Monday after suggesting in a weekend newspaper interview that being a mother made her a better candidate for the job. May has no children.
Leadsom, who was flanked by some of her supporters, said: "Strong leadership is needed urgently to begin the work of withdrawing from the EU. A nine-week leadership campaign at such a critical moment is highly undesirable."
She said May had the support of more than 60 per cent of Conservative MPs and was "ideally placed to implement Brexit on the best possible terms for the British people and she has promised she will do so".
Leadsom said she was "incredibly grateful" to the 84 colleagues who supported her leadership bid.
"Nevertheless, this is less than 25 per cent of the parliamentary party and after careful consideration I do not believe this is sufficient support to lead a strong and stable government should I win the leadership election," she said.
"There is no greater privilege than to lead the Conservative Party in government and I would have been deeply honoured to do it.
"I have however concluded that the interests of our country are best served by the immediate appointment of a strong and well-supported prime minister.
"I am therefore withdrawing from the leadership election, and I wish May the very greatest success."
The leadership contest is being overseen by the committee of backbench Conservative MPs.
Its chairman, Graham Brady, said May would be formally confirmed as the new party leader as soon as the Conservative Party board had been consulted -- saying there would be "no need to re-run the election".
He declined to give an exact timetable for the next steps -- other than to say it would not be "nine weeks" until Mr Cameron's successor was in place.
The contest was originally scheduled to finish on September 9.
The time between Gordon Brown winning the Labour leadership uncontested and succeeding Tony Blair as prime minister was 38 days.
Reacting to Leadsom's decision, Chris Grayling, May's campaign chief, said it showed what a "principled and decent politician she is".
Speaking outside the Houses of Parliament, he said May -- who is on her way back to London from Birmingham after her campaign speech -- was "enormously honoured" to be entrusted with the task of leadership, and would make a statement later.
In a message to the party, he said: "Now is the time for us to unite ... and get on with the job of securing a strong, prosperous future for our country."
Meanwhile, former London mayor Boris Johnson -- who was backing Leadsom's leadership bid, said he had "no doubt" May would be an "excellent" leader and prime minister.
There had originally been five contenders to succeed Cameron, with MPs voting in two rounds to get that number down to two -- and the plan then was that the party's 150,000-strong membership would have had the final say.
Labour, the Lib Dems and the Greens are calling for a snap general election, rather than waiting for the contest scheduled for 2020 under the Fixed Term Parliaments Act.
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