The government faces potential defeat on key amendments if rebel MPs from her Conservative party ally with the main opposition Labour party...
Lawmakers will have their first chance to scrutinise the EU Withdrawal Bill, which would formally end Britain's membership of the European Union and transfer four decades of EU legislation into UK law.
The government faces potential defeat on key amendments if rebel MPs from her Conservative party ally with the main opposition Labour party, increasing the risks for May's weak minority government.
Ministers say the legislation -- also known as the Repeal Bill -- would ensure legal certainty and avoid a damaging "cliff-edge" when Britain leaves the bloc in March 2019.
But critics warn it represents a power-grab by the government, while others see it as a chance to shape May's Brexit policy.
Scottish First Minister Nicola Sturgeon has also warned she will seek to block the bill unless changes are made to devolve more of the powers returned from Brussels.
She is meeting May at Downing Street later Tuesday, the first face-to-face talks between the two women since March.
"This bill is in the interests of everybody in the UK in terms of delivering the smooth Brexit that we want," the prime minister's spokesman said.
MPs have tabled almost 200 pages of amendments to the bill, which will be debated in groups over eight days spread over the coming weeks.
The showdown comes as May, weakened by a June election in which she lost her parliamentary majority, struggles to assert her authority over her own cabinet.
Two ministers have quit in the past fortnight -- one over sleaze, the other accused of effectively running her own foreign policy.
Meanwhile a report at the weekend suggested that two others, including leading eurosceptic Foreign Secretary Boris Johnson, are instructing May how to run Brexit.
Sterling dropped on Monday amid reports that dozens of Conservative MPs were backing a move to oust May.
She is also under increasing pressure from Brussels to come up with a financial offer to keep negotiations on track, with a crunch summit of EU leaders looming in mid-December.
Labour will seek a vote on Tuesday on an amendment to extend Britain's membership of the EU's single market and customs union, and the jurisdiction of the European Court of Justice, into a transition period.
The government said it wants an implementation period of around two years after Brexit but insists Britain will be fully out of the EU.
To that effect, it has tabled its own amendment putting the date of Britain's departure onto the face of the bill, which is also likely to be debated although not voted on Tuesday.
However, this has angered some Conservative MPs.
Former attorney general Dominic Grieve told AFP it was "utterly pointless and counterproductive" and would remove any flexibility in case the EU talks were delayed.
Another Conservative rebel, Anna Soubry, said the move had "really upset" a lot of people who did not normally speak out.
The toughest votes are expected in the coming weeks, as some Conservative MPs seek to reduce the powers the bill gives to ministers to change EU laws as they are transferred across.
Another flashpoint involves demands for a parliamentary vote on the final Brexit deal.
On Monday, the government made an apparent concession by promising a separate piece of legislation to authorise the final deal.
"We have listened, and will continue to listen," Brexit minister David Davis wrote to MPs.
However, he conceded that if the bill failed to pass parliament, Britain would still leave the EU on March 29, 2019 -- only without any deal at all.