Chair of 1922 Committee is reportedly planning to tell PM to leave by the end of June

Brexit talks between government ministers and Labour are due to resume on Tuesday amid distinctly limited expectations of a breakthrough, with the political focus likely instead to shift on to renewed Conservative efforts to oust Theresa May from Downing Street.

The executive of the 1922 Committee, which represents Conservative backbenchers, is scheduled to meet on Tuesday, with its chair, Graham Brady, reportedly planning to tell the prime minister she must depart before the end of June.

In the Brexit talks, a government team including David Lidington, May’s de facto deputy, and the Brexit secretary, Steve Barclay, is to meet Barclay’s Labour shadow, Keir Starmer, the shadow business secretary, Rebecca Long-Bailey, and others at the Cabinet Office.

Facebook Twitter Pinterest Government ministers including David Lidington, pictured, May’s de facto deputy, are to meet senior Labour figures. Photograph: Alkis Konstantinidis/Reuters

Other talks are scheduled, but none are as yet due to include May or Jeremy Corbyn. The Labour leader is scheduled to spend some of the first parliamentary day after the Easter recess meeting the young Swedish climate activist Greta Thunberg.

The talks were paused before Easter with Labour saying it had yet to hear a possible government compromise plan. The party has as yet only been given a time and location for Tuesday’s talks, with no sign of an agenda or any new offers.

With Brexit delayed until as late as 31 October at the recent EU summit, the immediate pressure to find a compromise plan has diminished slightly, and the political vacuum has immediately been filled by manoeuvres to remove May from No 10.

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Because she survived a no-confidence vote in December, triggered by enough Conservative MPs writing to the backbench 1922 Committee to request a challenge, May is officially safe under party rules for a year.

A series of reports have said the committee could instead pressure May, who has promised to step down once a Brexit deal is passed, to give a guaranteed date. ITV reported Brady was due to tell the PM that it should be no later than 30 June. But another committee source said no decisions had been made, and that most of the reports about attempts to remove May “have only reflected the views of one or two members”.

Sentiment among Tory MPs nonetheless seems to be shifting away from supporting the prime minister. One moderate MP said he thought it would be “sensible and logical” for Brady to pressure May to go soon.

“She seems to be mainly staying on out of a sense of stubbornness,” the MP said. “She has nothing more to offer the government or the country, so it seems time to turn the page on what has been a fairly dark chapter of events.”

Separately, May will face a no-confidence motion from a group representing Conservative grassroots members, it has emerged.

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The National Conservative Convention will be forced to call an emergency meeting to hear the motion next month after enough local party chairs signed a petition supporting the move, according to reports. Such a vote would be symbolic, but would place further pressure on May to go.

Before the resumption of Commons business, the senior Tory backbencher Nicky Morgan said the language used by some vehement Conservative Brexiters had helped to inspire threats against MPs.

The former education secretary criticised a Daily Telegraph article by her backbench colleague Bill Cash that accused May of having made an “abject surrender” to the EU, and talked also of “appeasement” and “capitulation”.

Asked if she saw a link between such phrases and the threats received by some MPs, Morgan said: “Yes, I do.” Such comments, she told the BBC, were “stoking up other people who are often sitting at home and watching this stuff, and it gets them really, really angry and fired up, and then they will say things that they would never say face-to-face”.