Pressure is growing on British Prime Minister Theresa May to set a date on when she will step down as cross-party Brexit talks were due to resume.

The prime minister was on Tuesday due to meet the chairman of the influential 1922 committee of backbench Conservative members of Parliament, Graham Brady, amid requests for clarity on her plans for triggering a leadership contest.

May had pledged to resign if and when Parliament approved her Brexit withdrawal agreement with the European Union — but she has not made it clear how long she intends to stay if no deal is reached.

Members are unable to trigger a formal vote of no confidence in the prime minister until December, however calls for May to go have ramped up in recent weeks.

The grassroots National Conservative Convention — the most senior body within the party — is to hold a vote of confidence in her leadership on June 15 when it holds an extraordinary general meeting.

The gathering of the 800-strong body of activists marks the first time in the party's 185-year history that a Tory leader has faced such action from its grassroots members.

According to the Daily Telegraph, the EGM motion will acknowledge that it has "been almost three years since we voted to leave and after two extensions to the original departure date, we no longer feel that Mrs May is the right person to continue as prime minister to lead us forward in the negotiations".

"We therefore with great reluctance ask that she considers her position and resigns, to allow the Conservative party to choose another leader, and the country to move forward and negotiate our exit from the EU."

Meanwhile, talks between the government and Labour over a possible Brexit deal were set to resume, with reports suggesting May could offer the opposition a temporary customs arrangement in a bid to break the stalemate, though it is understood the opposition will reject any agreement that stops short of a permanent customs union.

A senior minister told the Telegraph: "People are waiting to see what this deal is, if it happens. That will be the decision point for a lot of MPs when it comes to deciding the prime minister's future.

"It's going to be very difficult to support any deal Labour would support.

"It all comes down to the same old problem, that they want a full and permanent customs union, and we made a manifesto pledge to leave the customs union."

The UK had been due to leave the EU on March 29, but the deadline was pushed back to Oct 31 after Parliament was unable to agree a way forward.