Labour and the Conservatives were embroiled in a high-stakes row over whether to stage an immediate vote of no confidence in the government after the opposition chose not to table a binding vote on the issue on Monday night.

The opposition accused Downing Street of “running scared” because it had refused to allow time to debate an alternative, non-binding no-confidence vote in Theresa May as prime minister.

The Tories hit back, saying that Labour had “bottled it” by failing to exercise their right to force a no-confidence vote in the government when it looked like they might not win it.

Jeremy Corbyn had demanded a “vote of no confidence in the prime minister” at about 6pm after May told MPs she would delay holding the Brexit vote – which was pulled last week – to the week of 14 January.

The Labour leader said: “It’s bad – unacceptable – that we should be waiting almost a month before we have a meaningful vote on the crucial issue facing the future of this country.”

Play Video 1:22 Jeremy Corbyn announces he is tabling a motion of no confidence – video

But Labour deliberately chose a form of words that was different from that formally required to begin the process of trying to force a general election under the Fixed-Term Parliaments Act, arguing that if May were to be defeated, it would have “political force”.

The 2011 act says that a no-confidence motion must use the following text to be binding: “This house has no confidence in Her Majesty’s government.”

If submitted by the leader of the opposition, such a motion has to be debated the next day and, if the government were defeated, May would almost certainly have to resign. A new government would have to be formed in 14 days or else an election would take place.

Labour had the option of tabling a revised, binding confidence motion after Corbyn’s intervention until the Commons rose at 9pm but chose not to do so. A spokesman said the party would judge “day by day” when it was best to act..

The SNP and Liberal Democrats had indicated they would support Corbyn’s motion, but in the run-up to the close of business, it became clear that the DUP and Tory rebels were very unlikely to support any version of Labour’s motion, meaning it faced defeat.

Nigel Dodds, the leader of the DUP at Westminster, said its party would back May’s government for now while it tried to secure changes to her Brexit deal. Dodds said his MPs would not support “the antics of the Labour party”.

The hard-Brexit European Research Group, which is opposed to May’s proposed deal with Brussels, said its members would back May, even though they tried to oust her last week in a separate internal Conservative vote of no confidence in her leadership.

Steve Baker, a leading member of the ERG, said: “Eurosceptic Conservatives are clear that we accept the democratic decision in Theresa May as PM. We will vote against Labour in any confidence motion.”

At one point in the evening, it appeared that Downing Street would allow a debate on Corbyn’s motion to take place on Tuesday because it was confident of victory.

But that decision did not come about, and would have set a precedent for non-binding resolutions of no confidence to be debated immediately.

The SNP, Lib Dems and other minor parties swooped in as the Commons was rising for the night to put in their own amendment, which would have turned Corbyn’s motion into a formal vote of no confidence under the Fixed-term Parliaments Act.

However, that was not binding either, because by convention votes of no confidence have to be submitted by the leader of the opposition, as well as using the specified form of words.

Corbyn’s move came after an acrimonious debate on May’s stalled Brexit negotiations, in which the Labour leader had initially threatened to hold a confidence vote if she failed to name a date for the final vote after she pulled it last week. He briefed some journalists of his intention to do so shortly before 3pm.

The prime minister had appeared to have headed that off when she told MPs in a speech that began at 3.30pm that “we intend to return to the meaningful vote debate in the week commencing 7 January and hold the vote the following week”.

Corbyn initially withdrew the threat when he spoke immediately after May. Instead he said that the prime minister had “been dragged kicking and screaming to announce a date to restart the debate”.

That prompted accusations that he was not serious about trying to unseat the prime minister, and some senior Labour insiders complained that they had not been consulted about the plan, which at that point appeared to have backfired.

No 10 also said that Corbyn’s office had been aware of what May was going to say from about 3pm, when a copy of her remarks to MPs had been sent to him as a normal courtesy before a major Commons debate.

But Labour sources countered that their decision to call for a vote of no confidence in her as prime minister had been made before they had seen a copy of the text. Briefings about Corbyn’s plans had taken place shortly before 3pm.

On Tuesday, May is expected to step up warnings about the risks of a no-deal Brexit following a cabinet meeting in the morning and will ask cabinet ministers to press ahead with no-deal planning, allocating money from a £2bn contingency fund.

It marks the first steps in an attempt by May to persuade rebellious Tory MPs that the alternatives to her Brexit deal are worse before the meaningful vote in the week of 14 January.

May wants the increasingly serious no-deal preparations to dominate the Brexit discussion at cabinet, even though ministers worried about the stalled negotiations with Brussels are openly canvassing alternatives if her deal is voted down next month.

In the Commons on Monday, May told MPs in a tense and often acrimonious debate that a chaotic and economically costly no deal would happen – unless they voted for her deal, or parliament decided to abandon Brexit altogether.

No deal, the prime minister said, would “risk the jobs, services and security of the people we serve” at the price of “turning our backs on an agreement with our neighbours that honours the referendum and provides for a smooth and orderly exit”.

May also told MPs that negotiations were continuing between the UK and the EU, telling MPs that she was seeking “further political and legal assurances” over the unpopular Northern Ireland backstop, in an effort to demonstrate that it was temporary.

However, European commission officials in Brussels said that no further meetings between the EU and UK were taking place. “The deal that is on the table is the best and the only deal possible – we will not reopen it. It will not be renegotiated,” a spokesman said.