Two Labour MPs have submitted a motion of no confidence in Labour leader Jeremy Corbyn.
Margaret Hodge and Ann Coffey confirmed the move in a letter to the chairman of the Parliamentary Labour Party.
The motion has no formal constitutional force but calls for a discussion at their next PLP meeting on Monday.
It will be up to the PLP chairman to decide whether it is debated. If accepted it would be followed by a secret ballot of Labour MPs on Tuesday.
Earlier Mr Corbyn defended his role in the UK's EU referendum, in which Labour campaigned to Remain but ended in a vote to Leave by 52% to 48%.
The leader's critics said he was half-hearted in calling for Labour voters to unite behind Remain.
Dame Margaret said Mr Corbyn should resign because the EU referendum had been a "test of leadership" that he had "failed".
This left Labour voters "not getting a clear message", she added.
Dame Margaret is the MP for Barking and the former chairwoman of the Commons Public Accounts Committee, while Ms Coffey is the MP for Stockport.
Mr Corbyn said the point he had made during the campaign was that "there were good things" about the EU but also "other things that had not been addressed properly".
Former shadow chancellor Chris Leslie said there were "failures" in Labour's campaign, saying he would need "an awful lot of persuading to have confidence in Jeremy's leadership into a general election", while former minister Ben Bradshaw said he would support the no confidence motion.
In a leaked briefing note, Labour had told its MPs to say the party "best placed" to re-unite the country following the UK's decision to leave the EU.
The briefing note said Mr Corbyn was "uniquely placed" because he understood why many people had voted to leave.
Mr Corbyn won an overwhelming victory in last year's Labour leadership contest, but did not have the backing of most MPs.