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Green MP Caroline Lucas said it would be “unconceivable” for Labour to enter into such talks. 

Labour MP Paul Williams, meanwhile, called for all non-Brexit parliamentary business to be suspended. 

“There is nothing else more important than sorting this out,” he said. “I don’t think the public will understand why we are debating other stuff. 

“We should put deadlines on this process and if that means sitting at weekends then so be it. 

“By the end of the month, we need to provide businesses with certainty.” 

Plaid Cymru’s Westminster leader Liz Savile-Roberts, who co-ordinated the cross-party call for Labour to back a Brexit vote re-run, said: “Meaningless motions of no confidence tabled by the Labour Party on a rolling basis will do nothing but worsen the logjam and create further economic distress.

“We will not support efforts that only run down the Brexit clock – they must present a real chance of breaking the deadlock.” 

Williams, who also supports a second referendum, said he believed it to be a matter of time before the idea had a majority across parliament.  

“There are some MPs who want to try out some other options first but the problem with that is that we are massively running out of time,” he said.   

Plans for a soft Brexit would not succeed, Williams claimed. 

“I’m almost certain that it will fail,” he said.“It would be an establishment stitch-up. It would be a very small number of elite MPs getting together in a room, coming up with this plot to stay close to the EU and it is so out of touch. 

“We do need to reach out and see if there is a position that all MPs will back, but I think this process needs to happen within days not weeks.” 

There was also speculation on Thursday night that Labour could be facing frontbench resignations.  

Williams added: “I don’t think Jeremy Corbyn will whip for [a soft] Tory Brexit because I don’t think trade unions will back it. Trade unions want Labour MEPs in parliament arguing for better rights for British workers.”