The Labour leader, Jeremy Corbyn, has demanded that the prime minister give MPs the opportunity to vote on whether or not they have confidence in her after she delayed the showdown on her Brexit deal to January.

Corbyn tabled a motion of no confidence in Theresa May on Monday evening. While the government is not obliged to schedule a confidence vote before Christmas, the Labour leader said a refusal to do so would demonstrate that she was unable to command the confidence of the House of Commons.

Announcing his intention, Corbyn told the Commons it was “very clear that it’s bad, unacceptable, that we should be waiting almost a month before we have a meaningful vote” on May’s Brexit deal.

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Corbyn accused May of having “obdurately refused to ensure a vote took place on the date she agreed” and of further refusing to hold one before Christmas. Instead, May has said the Brexit vote will be held in the week commencing 14 January. “This is unacceptable in any way whatsoever,” Corbyn said.

He added that the motion he intended to table, aimed specifically at the prime minister and not at the government as a whole, was “the only way I can think of of ensuring a vote takes place this week”. As Corbyn went to sit down after finishing his remarks, May stood up and walked out of the chamber, nodding to the chair as she left.

Shortly afterwards, May was handed a boost when two prominent groups critical of her leadership indicated that they would back her, meaning Labour’s vote would almost certainly be defeated.

Steve Baker, a senior member of the Tory backbench and hard Brexit-supporting European Research Group, said: “Eurosceptic Conservatives are clear that we accept the democratic decision of our party to have confidence in Theresa May as PM. We will vote against Labour in any confidence motion.”

The Democratic Unionist Party also said it would back the prime minister, with its Westminster leader, Nigel Dodds, saying his MPs would not support “the antics of the Labour party”.

With the Tory right and the DUP pledging support, there were some indications last night that the government might allow the Labour motion to be debated swiftly – because Conservative whips were confident of winning.

Corbyn tabled an early day motion and, under parliamentary procedure, the government has the option of declining to clear any time in its own schedule for the business. In that case, the vote would have to be held on an opposition day, of which there are none remaining before Christmas, explained Dr Catherine Haddon, a senior fellow at the Institute for Government.

“If she refuses, it is clear that she does not believe she retains the confidence of this house,” Corbyn’s spokesman said.

Haddon said a motion of no confidence in the government under the Fixed-term Parliaments Act would force May’s hand.

The move came after May announced the revised date for the meaningful vote. Labour had promised to push for a no-confidence vote in the prime minister if she failed to name a date, so that threat seemed to have dissipated. But Corbyn announced his intention to table the motion as the debate closed.