Mr Corbyn tabled the motion after the prime minister gave the date for a Commons showdown on her Brexit deal as January 14, which she had already postponed at the eleventh-hour in the face of a catastrophic defeat.
Ahead of announcing the no confidence motion at the end of Ms May’s statement in the Commons, Mr Corbyn said she had “led the country into a national crisis", and lost the support of her own cabinet.
Later, No 10 said they would not table a vote on Mr Corbyn's no confidence motion, describing the move as playing "silly games".
See below for the day's developments
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Former Conservative minister Sam Gyimah has fired off angry messages accusing Theresa May of "displacement activity" designed to distract from her failed renegotiations.
Workers are to be given new protections as part of a major overhaul of workplace rights announced by the government.
Dozens of changes will be made to employment rules in a move ministers heralded as the “largest upgrade to workers’ rights in a generation”.
Work and Pensions Secretary Amber Rudd has said it was important to think about "how we test the will of parliament" over the Brexit deal.
She told Sky News: "My first point is that we need to get the withdrawal agreement through parliament. That has my full support and I hope that the PM will get the amendments, the changes that some of my colleagues seek.
"After that we need to find out where the will of parliament is, where the majority of MPs will vote in parliament and nothing should be off the table. We should consider all options."
A third cabinet minister has called for MPs to be allowed to break the Brexit deadlock through a series of votes on the options, as pressure grows on Theresa May to give way.
Greg Clark, the business secretary, said the Commons should be “invited to say what it would agree with” if – as seems certain – the prime minister’s deal is defeated.
Theresa May is due to give a Commons statement today at around 3.30pm, where MPs will be able to grill her over her trip to Brussels for the European Council summit on Thursday and Friday.
Expect a fairly fraught session, after Ms May's efforts to gain concessions were rebuffed. She was also captured on camera confronting Jean-Claude Juncker, the EU Commission chief, after he described the British Brexit position as "nebulous and imprecise".
Significantly, the words briefed overnight by Downing Street show the PM attempting to quash the prospect of a second referendum.
She is expected to say: “Let us not break faith with the British people by trying to stage another referendum.
“Another vote which would do irreparable damage to the integrity our politics, because it would say to millions who trusted in democracy, that our democracy does not deliver.
“Another vote which would likely leave us no further forward than the last.
“And another vote which would further divide our country at the very moment we should be working to unite it.”
On the agenda today, the Commons will sit at 2.30pm with Education Questions, before morning onto any urgent questions and a statement from the prime minister.
Former cabinet minister Justine Greening says a second referendum is the only way for Theresa May to break the deadlock on Brexit.
"A blocking group of MPs exists for every proposal," she said in a piece for the Financial Times, adding that 80-100 Tory MPs would be happy to pursue a no-deal scenario.
Ms Greening said there was no point in the PM "flogging her Brexit dead-horse deal any longer" and it was time to act. The delay was damaging the reputation of the UK and the Tory party, she said.
In non-Brexit news, an extra £12bn will be added to the UK's annual deficit after the statistics regulator ruled student loans unlikely to be repaid should count as government spending.
More here from our Education correspondent Eleanor Busby:
Independent MP Frank Field is planning to table a motion today to ask for a series of vote on different Brexit scenarios. While this motion is non-binding on the government, its a way of testing support among MPs for such a plan.
He said: "The public has a right to know how the House of Commons would vote on the different Brexit choices facing our country.
"I am trying to ensure we have an opportunity as soon as possible to register our vote on a range of options, including a reformed Northern Irish ‘backstop’, leaving the European Union without a deal, extending Article 50, entering into a future Norway- or Canada-style relationship with the EU, and holding a new referendum.
"The results of voting on each scenario wouldn’t be binding on the government.
"But they will test opinion to see if any way forward commands a majority amongst MPs. This could act as a powerful guide to the government during its ongoing discussions with the EU."
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