A tourist takes a photo on a smartphone as Pro-Brexit protesters hold onto placards as they demonstrate near the House of Parliament in London. Picture: Alastair Grant/AP

London - An influential lawmaker from British Prime Minister Theresa May's Conservatives urged her to make a statement at a crucial meeting on Wednesday on when she plans to step down, to help persuade rebels in the party to back her Brexit deal.

Nigel Evans, a joint executive secretary of the 1922 Committee of the party's 314 lawmakers, told the BBC that he had encouraged May "to give the timetable for her departure" in a planned speech to the group late Wednesday afternoon.

"A number of Brexiteers are reluctant to support her deal because they think, if it gets over the line, she will then say, 'Look what I've achieved, I'm staying,'" Evans told the broadcaster.

"A number of them want to make absolutely certain she's nowhere near the negotiating table when we start talking about the future trade relationship with the EU," he added.

"If the prime minister announces a timetable of departure, I think that's going to swing a lot of people behind her deal. We could get it over the line."

May promised in December to step down as party leader before the next general election, scheduled for mid-2022, but most Conservative lawmakers expect her to leave her post long before then.

She met her cabinet earlier Tuesday as she tried to save the Brexit deal she has agreed with the EU, ahead of planned "indicative votes" on alternatives by lawmakers from Wednesday.

May was hit late Monday by the resignation of three more junior ministers, who joined 27 other Conservative rebels in voting with the opposition for a say on alternatives to her deal.

A Downing Street spokesman said following the cabinet meeting that May planned to "engage constructively" with the voting process and could still hold the third "meaningful vote" on her Brexit deal this week, if it can build enough support among lawmakers.

May had been expected to table a third vote on the Brexit deal this week, after parliament twice rejected it by a large margin.

She told lawmakers on Monday that there was "still not sufficient support" for her to hold the third vote.

The options for indicative votes are expected to include a second referendum on EU membership, and deals that would keep Britain in a much closer relationship with the EU than the one negotiated by May.

May said she would not commit the government to acting on the results of those votes.

Several Conservative lawmakers urged her to resign on Monday.

Since the EU agreed May's request for a short delay to Brexit last week, many eurosceptic Conservatives have pushed harder for a no-deal Brexit.

Sammy Wilson, Brexit spokesman for Northern Ireland's Democratic Unionist Party, wrote for The Daily Telegraph on Tuesday that his party remains opposed to May's "toxic deal."

In better news for May, Jacob Rees-Mogg, who leads a group of some 80 eurosceptic Conservative lawmakers, suggested he could now back her deal.

"The choice seems to be Mrs May's deal or no Brexit," Rees-Mogg tweeted.