Pro-leave cabinet members are to meet on Monday to discuss Theresa May’s proposed deal to leave the EU amid calls from backbenchers that they should resign to force a change in policy or a change in leader.

Andrea Leadsom, the House of Commons’ leader, has convened a meeting of the so-called pizza group, which will discuss Dominic Raab’s return from Brussels without an agreement.

The international trade secretary, Liam Fox, the international development secretary, Penny Mordaunt, the work and pensions secretary, Esther McVey, and the transport secretary, Chris Grayling, have in the past attended their meetings.

The faction, nicknamed after their previous choice of takeaway meals, has also been joined by the home secretary, Sajid Javid, at past meetings, informed sources said.

Brexiters on the backbenches piled pressure on the ministers on Sunday to step down from office. Mark Francois, the vice chair of the pro-Brexit European Research Group, described the UK’s chief Brexit negotiator Ollie Robbins as a “Svengali” and called on cabinet ministers to leave government.

“This process is now being driven by a small number of pro-EU civil servants in No 10 led by Ollie Robbins, who appears to be the PM’s Svengali on all things European,” he said. “We believe that now is the time for members of the cabinet to finally stand up and be counted.”

Fellow Brexiter Andrea Jenkyns tweeted that Brexiters in government should now step down.

It is better to go down fighting and honouring the democratic decision of our British people. Then to be long remembered for waving a white flag and surrendering to EU demands. All Brexiteers in Gov and on the backbenches its time to #StandUp4Brexit and finally #ChuckChequers. — Andrea Jenkyns MP #StandUp4Brexit (@andreajenkyns) October 14, 2018

David Davis, the former Brexit secretary, called on cabinet ministers to rebel against May’s proposed deal to leave the EU, as the government prepares for a key summit with Europe’s leaders.

Writing in the Sunday Times, Davis said the plan to could keep the UK in a customs union to avoid a hard border with Ireland was “completely unacceptable” and urged cabinet ministers to “exert their collective authority”.

Nadine Dorries, the Conservative backbencher, backed his intervention and suggested he should become “interim leader” to deliver Brexit. She said: “His position has always been change the policy, not the PM. Getting May out and him becoming an interim leader may be the only way to deliver Brexit and [a free-trade agreement].”

Sources close to Davis sought to dampen the speculation, saying he was unlikely to “volunteer for the worst job in the world”.

Quick Guide Who are the main pro- and anti-Brexit groups? Show Pro-Brexit - European Research Group The long-established coalition of Brexit-minded Conservative MPs – though it publishes no list of members – led by Jacob Rees-Mogg, and one of Theresa May’s main obstacles in parliament. Leave Means Leave Headed by the businessman Richard Tice, and newly joined by Nigel Farage, this group seeks a Brexit completely outside any single market, customs union or EU oversight. Change Britain The successor group to the official leave campaign, it is headed by Labour MP Gisela Stuart, and says it wants to see the referendum result “respected and delivered in full”. Stand Up 4 Brexit A new group campaigning to sink May’s Chequers proposals, which claims the support of 20 Tory MPs, among them Priti Patel and Iain Duncan Smith. Leave.EU The unofficial leave campaign, financed by Arron Banks, which faces scrutiny about its tactics and funding. These days mainly a Twitter feed that mixes Brexit news with far-right-friendly messages about immigrants and Islam. Soft Brexit/remain - Open Britain Springing up in the wake of the referendum, this grouped MPs from various parties in pushing for a soft Brexit. It was supported by some Tories, such as Anna Soubry and Dominic Grieve, but they cut ties over a plan to oust hard Brexit-backing MPs. Best for Britain A later arrival, chaired by the former Labour minister Mark Malloch-Brown, this is more directly opposed to Brexit itself, and has received funding from the billionaire George Soros. People's Vote Part of Open Britain, this group calls for a referendum on the final Brexit deal. European Movement A long-established pro-EU group with sections across Europe, this has had a lower-profile role in the Brexit aftermath. Chaired by ex-Conservative cabinet minister Stephen Dorrell. Our Future Our Choice Set up by and seeking to represent young people, the group organises protests, and is probably best known for its eloquent spokesman Femi Oluwole. For Our Future’s Sake Going by the handy acronym of FFS, this is a student-based group seeking to block Brexit. Scientists for the EU A self-explanatorily named niche pressure group with a heavyweight set of scientific backers.

May is also under pressure from Europhile Tories over the backstop agreement. Ruth Davidson, the pro-EU leader of the Scottish Tories, and her ally David Mundell, the Scottish secretary, have told May in writing they would resign their positions if there was a hard border between Northern Ireland and the UK after Brexit.

“[We] could not support any deal that creates a border of any kind in the Irish Sea and undermines the union or leads to Northern Ireland having a different relationship with the EU than the rest of the UK, beyond what currently exists,” they wrote.

The shadow Brexit secretary, Keir Starmer, said it was “deeply disappointing” that no deal had been reached and warned that Raab risked signing up to a plan that would ultimately be scuppered by the House of Commons unless the government allowed the UK’s proposals for the backstop to be scrutinised.

“The details of any proposed backstop agreement need full and searching scrutiny in parliament, not least because the final deal will need parliamentary approval,” Starmer said. “I would therefore urge the prime minister to publish the latest backstop proposal today – alongside an oral statement – to provide sufficient time to scrutinise and debate it.”