The dispute has seen key figures in the shadow cabinet demanding that the party strike sooner rather than later in order to remove the prime minister from office after she was weakened by an attempt by Tory MPs to oust her.
But Mr Corbyn and his allies are refusing to allow the offensive to go ahead until there is a good chance it will be successful, and are likely to block any attempt to move until Ms May has held her meaningful vote on her Brexit deal. They believe the Tory Brexiteers and the DUP are not yet ready to vote with the opposition parties to topple the government.
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The Independent understands that those backing swift action include Tom Watson, Labour’s deputy leader, and Sir Keir Starmer, the influential shadow Brexit secretary, while those backing Mr Corbyn’s decision to play the waiting game include shadow chancellor John McDonnell, shadow international trade secretary Barry Gardiner, shadow foreign secretary Emily Thornberry, shadow education secretary Angela Rayner and party chairman Ian Lavery.
Labour sources would not rule out tabling a no-confidence motion this week, after Ms May addresses the Commons on the latest Brexit negotiations, but the party is understood to be more likely to strike once Ms May brings her deal back to the Commons in January.
One source said: “We’re taking it on a day-by-day basis, but January is the most likely.
“It partly depends what happens on Monday, though. If the Tories and DUP tear strips off her than that could be the time for us to move.”
As well as calls from within the shadow cabinet, Mr Corbyn is also facing mounting pressure from his backbenchers and party members to act now.
MPs frustrated at the lack of action have set up a new WhatsApp group named “The Sanity Group” to coordinate how to push him to strike before Christmas.
At the same time, a group from the 2017 intake of Labour MPs is coordinating a private letter to Mr Corbyn urging him to act swiftly.
Most of the MPs pushing for action before Christmas are supporters of the campaign for a fresh Brexit referendum.
Labour’s official policy is that it will only consider backing another public vote once attempts to topple the government and trigger a general election have failed. Many of the party’s MPs believe this is inevitable and want the process sped up so that focus can be shifted towards fighting to give voters a Final Say referendum.
The issue of when to table the motion of no confidence was the subject of a lengthy discussion at Tuesday’s shadow cabinet meeting, with Mr Watson leading calls for the party to strike before Christmas.
A shadow cabinet source said: “Tom Watson was pushing for it to happen quickly but he was shut down straight away.
“He’s in the camp of MPs that just wants a People’s Vote. It was clearly political and that view was the minority.”
Sir Keir is also understood to be pushing for a motion to be tabled quickly. The shadow Brexit secretary is widely seen to be more favourable to a second referendum than some in Mr Corbyn’s team.
Another source said: “Tom and Keir were saying it was imperative for the opposition to hold the government to account when it has clearly lost control and there is no obvious solution.”
Mr Watson and Mr Starmer reportedly urged the need for political leadership, arguing that Ms May’s decision to delay the “meaningful vote” on the Brexit deal clearly showed the prime minister did not have the confidence of parliament.
They are also understood to have insisted the party could table one motion now and one in January, highlighting that there were numerous attempts to bring down the Callaghan government in the late Seventies.
The SNP is also piling pressure on Labour to table the confidence motion, while party members and dozens of MPs are also calling for swift action.
Mr Corbyn will face mounting pressure to act after Ms May addresses the Commons on her talks with EU leaders last week. The prime minister is likely to be forced to admit she has not been able to secure compromises from the EU on the withdrawal agreement, fuelling anger among Tory backbenchers and the DUP.
On the issue of when the motion should be tabled, one senior shadow cabinet minister said: “It’s all about timing. There are 117 of her MPs who have said they have no confidence in her, and it would only take a few to vote with us. But it’s a case of when.
“The DUP will be key. They’re saying they won’t vote no confidence at the moment but if she comes back from Europe with f*** all then I think that could change.”
As the internal row spilled into the public eye, one of those pushing for the process to be sped up said: “What is the point of an opposition if we’re just going to sit on our hands for a month? People are looking to Labour for leadership and they’re not getting any, and that’s the bare truth of it.
“On Monday she’ll come back to the Commons after her tour of Europe and she won’t have anything at all meaningful to show for it. That’s obviously the logical point to table the no-confidence vote.”
Another MP angry at the delay added: “Jeremy is more focused on his root vegetables than he is on bringing down the government. He is nowhere to be seen. We’re just faffing around.
“He knows that as soon as the motion falls, we’re going to be demanding we move on to the next stage of our official policy which is campaigning for a People’s Vote.
“It has got to happen sooner rather than later. You can table these things as often as you like – there’s no reason not to do one now and one in January. We’ve got to get on with this to show some leadership and oppose the government.”
Party divisions were deepened last week when dozens of MPs who back a fresh vote on Brexit signed a public letter demanding Mr Corbyn table the no-confidence motion immediately. The letter was raised at shadow cabinet and condemned, with ministers suggesting it was a crude attempt to push Labour into supporting a fresh Brexit referendum.
One shadow cabinet minister told The Independent: “The people pushing for a no-confidence vote now have no interest in a no-confidence vote. It’s all about trying to bring about another referendum.”
Another shadow cabinet source added: “There was a lot of anger about it.”
Mr Corbyn is also under pressure from other opposition parties. The SNP, Liberal Democrats, Plaid Cymru and the Green Party have invited him to a meeting where they are likely to demand he table a motion of no confidence. The SNP is understood to be ready to do so if he refuses, although the government would be able to dismiss a motion not tabled by the official opposition.
Despite Labour’s main priority being to strike when it has most chance of winning, there is also concern in some parts of the party about what could happen if it did succeed in ousting Ms May.
Party figures have seen the problems the current prime minister has encountered while trying to navigate Brexit amid opposition from ardent backbenchers, and fear Mr Corbyn could face the same fate if he entered No 10 with a small majority before Britain leaves the EU.
“We need to let them get Brexit over with first,” one shadow cabinet source said.
But one MP backing the campaign for a fresh referendum and pushing for Labour to table the no-confidence motion this week said: “We need this to happen soon or we’ll run out of time to have the idea of a People’s Vote put to a proper vote in the House of Commons. At this rate we’ll get to 29 March and the Labour leadership will finally say it is going to fulfil the rest of the motion agreed at conference, and it will be too late.
“Unless the DUP radically change their position there is no way we’re going to win a vote of no confidence. Delaying it by saying you might win it further down the line is just an excuse for doing nothing.”
A spokesperson for Mr Corbyn said: “It’s a question of when, not if. We will seek a general election at the best moment and we will judge that day by day, week by week.”
Despite having so far resisted a no-confidence process that many fear would culminate in defeat and Labour being forced to instead support a fresh referendum, The Independent understands that members of Mr Corbyn’s team are increasingly of the view that they will eventually have to bow to pressure to give the public a Final Say vote.
They are unlikely to do so, however, until all other options are exhausted, and certainly not before MPs have voted on Ms May’s deal.
Those involved in discussions said that even if attempts to force a general election fail, Labour will not immediately pivot to backing a public vote.
One source with an understanding of the leadership’s position said there are “powerful institutional forces”, including trade union leader Len McCluskey, a number of shadow ministers and dozens of MPs, strongly opposed to a fresh public vote.
“It’s heading in that direction and I think it is probably inevitable, but a lot of influential people are still very opposed to it,” they said.
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.