LONDON, May 7 (Xinhua) -- British Prime Minister Theresa May's future at 10 Downing Street was slated to be at the top of the agenda at a crunch meeting Tuesday with the chairman of the Conservative Party's committee of backbench MPs.

Widespread media reports in London said Sir Graham Brady, chairman of the 1922 Committee is expected to press May to name a proposed date when she will step down as leader of the party, effectively meaning calling an end to her time as prime minister.

The fresh impetus by Brady follows concerns raised by a number of Conservative MPs over talks also due on Tuesday between May's government and the main opposition Labour Party to strike a Brexit deal.

Both parties have been engaged in weeks of behind-closed-doors talks in a bid to break the deadlock that has so far prevented the House of Commons from agreeing a deal that would pave the way for Britain to leave the European Union.

Labour has insisted it wants a deal that will keep Britain linked to the EU's Customs Union and Single Market, but the Conservative Party's policy has been that membership of both bodies should end to enable Britain to strike global trading deals.

One of May's strongest critics, MP Bill Cash, a leading Eurosceptic, commented: "The time has come for her (May) to resign. She needs to be given a date. The sooner the better. But it needs to be done in an orderly manner."

In a separate blow for May, the body representing local level Conservative associations across the country has called an emergency convention meeting mid-June to hold a no-confidence vote in May.

Britain's Foreign Secretary Jeremy Hunt said in a radio interview Tuesday that both sides in the Brexit talks between the Conservative Government and Labour need to be willing to compromise.

Britain's Education Secretary Damian Hinds said in a breakfast television that people should not "read too much" into the timing of the May's meeting with Brady.