Jeremy Corbyn will face a leadership challenge, probably within the next 72 hours, as talks about whether he can be persuaded to resign run into the sand.

The former Shadow Business Secretary Angela Eagle has the 50 nominations she needs from fellow Labour MPs or MEPs to launch a leadership challenge, and has a team in place to run her campaign.

“She will challenge him,” one of her allies said. “She has absolutely got the 50 names that she needs. She has got really strong support. We’re not putting a date on it, because we’re still hoping Jeremy might come to his senses - but there’s no sign of it.”

Mr Corbyn’s supporters are buoyed by the huge increase in Labour Party membership. They believe that the majority of the 113,000 who have signed up since the referendum have joined to give him their support, despite the overwhelming vote of no confidence he received from Labour MPs – though others have signed up so that they can vote to remove him.

Mr Corbyn has also received motions of support from constituency parties, including one last week from Angela Eagle’s Wallasey constituency. But other local parties have backed the MPs who have declared no confidence in him. There were motions calling on Mr Corbyn to resign in two wards in his own Islington North constituency this week, both of which were narrowly defeated.

Once a leadership campaign has kicked off, Labour’s national executive will have to rule on the highly controversial question of whether Mr Corbyn has to find 50 Labour MPs or MEPs prepared to sign his nomination papers. Given how few supporters Mr Corbyn has left among Labour MPs and MEPs, he might struggle to find 50 who are prepared to nominate him.

Mr Corbyn’s office have obtained a legal opinion which says that he has an automatic right to stand for re-election if challenged, but Labour’s general secretary, Iain McNicol, has also consulted a lawyer and is reputed to have been given the opposite advice.

Labour’s Deputy Leader, Tom Watson, is still locked in prolonged and inconclusive negotiations with union leaders, with no obvious prospect that they can come to an agreement. The union bosses say that any deal must be on the basis that Mr Corbyn continues in office, while Mr Watson has told them that the leader has irretrievably lost the confidence of his MPs and any deal must include him stepping down.

Independent