A leadership contest can be triggered in two ways: If 15 per cent of Conservative MPs write to the chairman of the 1922 Committee expressing they no longer have confidence in the party leader, or if the current leader resigns.
The vote is then thrown open to the Tories' 160,000 members who spend a month deciding who will lead their party - and thus be the next prime minister.
The deadline for nominations is Monday.
British opposition leader Jeremy Corbyn, celebrating Labour's win in the Peterborough by-election hours later, repeated his call for a general election to stop the Conservatives bringing in a no-deal option.
On Friday he tweeted that the next leader should let the people decide the UK's future.
Her team has been keen to shape her legacy beyond the Brexit failure, but she bequeaths to her successor a nation where traditional political divides are being eroded by strong beliefs on whether Britain should leave the European Union, and how it should do so.
Official nominations to replace her will be received on Monday, and Conservative Party grandees want the selection process to be completed by the end of July.
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Labour candidate Lisa Forbes secured a narrow majority of 683 votes over Nigel Farage's new party, as the Conservatives fell back into third place.
She put on a courageous face this week when hosting US President Donald Trump for a state visit, before joining him and other world leaders to mark 75 years since the D-day landings.
The Conservative leadership contest risks deepening the rift in the party over when, how or even if to leave the European Union - with a few of the almost dozen contenders ruling out serving in a future cabinet - if they are vanquished and lose out to a rival. "So, the first issue a new prime minister has to make clear is what are they going to do with the Withdrawal Agreement that is there", said Rutter.
"The Conservative Party has utterly failed the country over Brexit and is unable to improve people's lives or deal with their most pressing needs", said the Labour leader.
At the party's first national conference on June 30th in Birmingham, Mr Farage has said that he and his team will unveil the direction of their policy development, adding: "Then we will start a consultation with our paying supporters - all 110,000-and-counting of them - and give them a vote on what happens next".
Under the timetable set out by the party high command, it is expected the new leader will be in place in the week beginning July 22, following a postal ballot of the party members.
With the worst performers eliminated each time, the goal is to have two candidates left by 20 June.