Theresa May is facing demands she announce her resignation as prime minister as soon as today.
Tory MP Nigel Evans, the joint executive secretary of the party’s backbench 1922 Committee, said the process of finding a replacement for May “can’t start soon enough”.
“To be honest I would be delighted if she announced today she was announcing her resignation and we could then have an orderly election to choose a new leader of the Conservative Party,” he told BBC Radio 4′s Today programme on Tuesday morning.
“I believe the only way we’re going to break this impasse properly is if we have fresh leadership of the Conservative Party,” the senior Tory added.
“If there was an announcement today by the prime minister then of course we could start the process straight away.”
May, who will hold a meeting of the cabinet today, has promised to step down as soon as the first stage of the Brexit process is completed.
But with little sign a deal is about to be agreed, she is under renewed pressure to quit sooner.
The executive of the 1922 committee is due to meet today to discuss changing party rules to allow May to be ousted sooner than currently permitted.
Following the failed coup against her last year, the PM can not be forced out until December.
On Monday it emerged May could face an unprecedented vote of confidence in her leadership after 70 local Conservative association chiefs signed a petition in support of a poll.
They called for an extraordinary general meeting of the National Conservative Convention to discuss the PM’s leadership of the party.
Elsewhere a new poll found former foreign secretary Boris Johnson is the favourite to replace May as Conservative leader among the party’s grassroots.
Almost a third of party members – 32.4% – backed the pro-Brexit Tory to take over the helm of the party, up by 10 points in the last month.
Ex-Brexit secretary Dominic Raab was second with 14.7%, according to the poll of 1,128 panel members by the Conservative Home website.
Environment Secretary Michael Gove, who also supported the Leave campaign, came third, ahead of Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid.