Theresa May has formally postponed the vote on her Brexit deal, telling MPs it was clear that concern among them about the Irish backstop proposals would have led to it being rejected “by a significant margin”.

The vote would not proceed “at this time” and be deferred, May told a packed and noisy House of Commons, giving no details as to when it would take place. No 10 subsequently indicated it might not take place until January.

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The prime minister said that in the interim she would return to EU member states to seek “further assurances” on the backstop, and seek ways to “empower” the Commons.

May will continue on a frantic round of European diplomacy in an attempt to obtain a written text that she will be able to present MPs, but a breakthrough is not expected this week, even though the PM will end it by going to Brussels for a scheduled summit of EU leaders on Thursday and Friday.

Jeremy Corbyn, responding to May’s statement, said the country was in “an extremely serious and unprecedented situation”. The Labour leader argued it would be pointless to bring what was fundamentally the same deal back to the house, whether in a few days or next month.

The CBI said the delay to the deal was a blow for business, and that the UK “risks sliding towards a national crisis”.

The decision to stop the Commons voting after three of five planned days of debate on the deal prompted a furious intervention from the Speaker. John Bercow said that while the government could unilaterally pull the vote, it should reconsider doing so at an “inordinately late stage”.

Downing Street said it would pull the vote formally at around 8pm tonight, when the Commons clerks call out the business to be debated. A government whip simply has to shout “tomorrow” for the business to be deferred indefinitely; No 10 said the procedure was a standard one used all the time.

May began her address by saying that during the debate she had “listened very carefully to what has been said in this chamber and out of it by members of all sides”, prompting laughter from many MPs.

“From listening to these views it is clear that while there is broad support for many of the key aspects of the deal, on one issue, the Northern Ireland backstop, there remains widespread and deep concern,” she said.

“As a result, if we went ahead and held the vote tomorrow, it would be rejected by a significant margin.”

Quick guide Brexit and backstops: an explainer Show Hide A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

May said that before the European council summit later this week, she would visit her counterparts in other member states, as well as the leadership of the European council and the commission. “I will discuss with them the clear concerns that the house has expressed.”

May said she believed it was still possible to secure a majority for her deal in parliament, “if I can secure additional reassurance on the question of the backstop, and that will be my focus in the days ahead”.

“If you take a step back, it is clear this house faces a much more fundamental question: does this house want to deliver Brexit?” May asked, to shouts of “No!”.

She continued: “If the house does, does it want to do so through reaching an agreement with the EU? If the answer is yes, and I believe that is the answer of the majority of this house, then we all have to ask ourselves whether we’re prepared to make a compromise. Because there will be no enduring and successful Brexit without some compromise on both sides of the debate.”

Corbyn said it had been “evident for weeks” that MPs would reject the deal. “The government has lost control of events and is in complete disarray.”

He asked May to clarify if she was seeking actual changes to the withdrawal agreement with the EU, or “mere reassurances” about change.

“Bringing back the same botched deal, either next week or in January – and can she be clear on the timing? – will not change its fundamental flaws and deeply held objections right across this house, which go far wider than the backstop alone,” he said.

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There was, however, no indication when May would return. Asked by the Scottish National party’s Kirsty Blackman when a vote. The prime minister said that under the EU Withdrawal Act if no deal had been agreed with the European Union by 21 January she must make a statement to parliament.

But it understood that the conditions set out in the act have already been met because the UK has already negotiated a Brexit deal in principle with the EU. Technically, the meaningful vote could be held on any date, although in practice this will be limited by the government’s ability to get through the ensuing legislation required to ratify the deal through parliament.

Asked about this possibility in the debate by former education secretary Justine Greening, May discounted it, but declined to say when she would return.

Bercow said: “Halting the debate after no fewer than 164 colleagues had taken the trouble to contribute will be thought by many members of this house to be deeply discourteous.”

However, the Speaker said that while his procedural advice was that the government could decide on its own to delay the vote, it was “infinitely preferable” to give the house the opportunity to vote on whether the debate should be adjourned.

“I can reassure ministers that I would be happy to accept such a motion so that the house can decide,” he said.

He said the alternative would mean the Commons was “not only deprived of its opportunity to vote on the substance of the debate tomorrow but also given no chance to express its view today on whether the debate should or should not continue”.