Talks between the government and Labour on Brexit have resumed as MPs return to Westminster following the Easter break.
Cabinet ministers are meeting senior opposition figures in an attempt to solve the impasse by finding a deal that could win the support of MPs.
But some Tory MPs are angry the talks with Labour are even taking place.
Leading backbencher Nigel Evans called on Theresa May to step down as prime minister “as soon as possible”.
Cross-party meetings have been going on for a number of weeks after Mrs May’s EU withdrawal deal was rejected for a third time by MPs.
Arriving for the talks at the Cabinet Office, shadow Brexit secretary Sir Keir Starmer said “fundamental issues” remained between Labour and ministers on a number of key issues.
“We’ve been exchanging correspondence with the government but now we want to know what is their position on the issues that remain between us,” he said.
Sir Keir was accompanied by shadow chancellor John McDonnell, shadow business secretary Rebecca Long-Bailey and shadow environment secretary Sue Hayman.
Theresa May’s de facto deputy David Lidington is expected to lead the talks for the government.
BBC assistant political editor Norman Smith says most people at Westminster seem to take the view that the prime minister is clutching at straws by pinning her hopes on reaching an agreement with Jeremy Corbyn.
He says Labour’s position has not changed and Mrs May will have take a political decision to accept a customs union with the EU if she is to get Mr Corbyn to sign off her plans.
If she does that, our correspondent added, it would almost certainly provoke a cabinet walkout and open warfare on the backbenches.
‘Praise not blame’
Senior members of the influential backbench 1922 committee of Tory MPs are meeting to discuss, among other things, whether steps should be taken to try to change the rules which currently prevent Conservatives calling another no-confidence vote in Mrs May until December.
The group’s joint executive secretary and MP for Ribble Valley Mr Evans told BBC Radio 4’s Today programme earlier the calls for the prime minister to quit had become “a clamour”.
“The only way we’re going to break this impasse properly is if we have fresh leadership of the Conservative Party,” he said.
He said Mrs May “had been reaching out to the Labour Party and Jeremy Corbyn, when she should have been reaching out to the people”.
But Prisons Minister Rory Stewart said Theresa May was doing a “good job” and deserved “praise not blame”.
“The idea somehow that some new fresh leader with extraordinary charm and nimble feet would be able to suddenly get the deal across the line is mistaken,” he told the BBC.
“It’s nothing to do with the individual, it’s that people disagree deeply about Brexit.”
Mr Evans’s comments came after it emerged that Mrs May faces a no-confidence challenge from Tory campaigners.
More than 70 local association chiefs have called for an extraordinary general meeting to discuss her leadership and a non-binding vote is to be held at the National Conservative Convention EGM in May.
If the grass-roots Tory vote showed a lack of confidence – it could put greater pressure on the 1922 Committee to find some way of forcibly removing the PM from office.
That pressure could increase further if the Tories poll badly in local and European elections on 2 and 23 May respectively.
Meanwhile, Change UK has launched its European election campaign in Bristol, while Nigel Farage’s Brexit Party has unveiled more of its candidates in London.
Change UK is made up of 11 former Labour and Tory MPs who quit their parties in February.
This means the UK is likely to hold European Parliament elections on 23 May.