LONDON - British Prime Minister Theresa May was under pressure on Monday to give a date for leaving office as the price to bring Brexit-supporting rebel lawmakers in her party behind her twice-defeated European Union divorce treaty.

At one of the most important junctures for the country in at least a generation, British politics was at fever pitch and, nearly three years since the 2016 EU membership referendum, it was still unclear how, when or if Brexit will ever take place.

With May humiliated and weakened, ministers lined up to insist she was still in charge and to deny a reported plot to demand she name a date to leave office at a cabinet meeting at 1000 GMT on Monday.

"Time's up, Theresa," Rupert Murdoch's Sun newspaper said in a front page editorial. It said her one chance of getting the deal approved by parliament was to name a date for her departure.

"I hope that the cabinet will tell the prime minister the game is up," Andrew Bridgen, a Conservative lawmaker who supports Brexit, told Sky News.

"The prime minister does not have the confidence of the parliamentary party. She clearly doesn't have the confidence of the cabinet and she certainly doesn't have the confidence of our members out there in the country," he said.

Ministers will discuss at 0900 GMT how to address parliament's attempts to take control of Brexit before a meeting of May's cabinet team, a government source said.

The United Kingdom, which voted 52-48 percent to leave the EU in the referendum, remains deeply divided over Brexit.

Just 24 hours after hundreds of thousands of people marched through London on Saturday to demand another referendum, May called rebel lawmakers to her Chequers residence on Sunday in an attempt to find a way to break the deadlock.

"The meeting discussed a range of issues, including whether there is sufficient support in the Commons to bring back a meaningful vote (for her deal) this week," a spokesman for May's Downing Street office said.

Boris Johnson, Jacob Rees-Mogg and Steve Baker attended along with ministers David Lidington and Michael Gove who had been reportedly lined up as caretaker prime ministers. They were forced on Sunday to deny they wanted May's job.

MAYDAY

May was told by Brexiteers at the meeting she must set out a timetable to leave office if she wants to get her deal ratified, Buzzfeed reporter Alex Wickham said on Twitter.

May told the lawmakers she would quit if they voted for her twice-defeated European Union divorce deal, ITV news said.

The Sun's political editor, Tom Newton Dunn, said some ministers were urging May to pivot to a no-deal Brexit as the only way to survive in power.

The deal May negotiated with the EU was defeated in parliament by 149 votes on March 12 and by 230 votes on Jan. 15.

To get it passed, she must win over at least 75 MPs - dozens of rebels in her Conservative Party, some opposition Labour Party MPs and the Northern Irish Democratic Unionist Party (DUP), which props up her minority government.

The Sunday Times reported 11 unidentified ministers agreed May should stand down, warning she has become a toxic and erratic figure whose judgment has "gone haywire".

Brexit had been due to happen on March 29 before May secured a delay in talks with the EU. Now a departure date of May 22 will apply if parliament passes May's deal. If she fails, Britain will have until April 12 to offer a new plan or decide to leave without a treaty to smooth the transition and avoid an economic shock.

Lawmakers are due on Monday to debate the government's next steps on Brexit, including the delayed exit date. They have proposed changes, or amendments, including one which seeks to wrest control of the process from the government in order to hold votes on alternative ways forward.

Amendments are not legally binding, but do exert political pressure on May to change course.

(Additional reporting by Kate Holton, William Schomberg, David Milliken and Andrew MacAskill; Writing by Guy Faulconbridge; Editing by Janet Lawrence) ((guy.faulconbridge@thomsonreuters.com; 07825218698;))