Theresa May has suffered a second humiliating defeat on her Brexit deal, as MPs voted it down by a crushing majority of 149, dealing a fresh blow to her shattered authority.

With just 17 days to go until the UK is due to leave the EU, backbenchers from both sides of the Brexit divide immediately began manoeuvring to take control of the next steps of the process, in a series of key votes in the coming days.

MPs ignored the prime minister’s pleas to “get the deal done” and voted the deal down for a second time, after the Democratic Unionist party (DUP) said it was not convinced by last-minute assurances won from Brussels on Monday.

Of the Conservatives who rejected the deal in January, when May lost by a record majority of 230, 39 switched sides, including the former Brexit secretary David Davis – with many fearing Brexit would be delayed or reversed if they did not support the agreement.

All but three Labour MPs trooped through the packed voting lobbies with the DUP, the pro-Brexit European Research Group (ERG), and some remain-supporting Tories, to sink May’s plan.

In total, 75 Conservatives rebelled, and the deal was rejected by 391 votes to 242.

With her voice cracked and fading, the prime minister had earlier pleaded with the House of Commons: “This is the moment and this is the time – time for us to come together, back this motion and get the deal done. Because only then can we can get on with what we need to do, what we were sent here to do.”

After the catastrophic defeat, May immediately rose to her feet to say she “profoundly regretted” that her deal had been rejected for a second time.

May makes final appeal to MPs ahead of crucial Brexit deal vote Read more

She said MPs would be given the opportunity to debate on Wednesday whether the UK should leave the EU without a deal on 29 March – and that she would offer MPs a free vote on that decision.

They will then be given the opportunity to delay Brexit, by requesting an extension to article 50, on Thursday.

The prime minister said she had “personally struggled” with the question of no deal, but said: “I am conscious also of my duties as prime minister of the United Kingdom of Great Britain and Northern Ireland and of the potential damage to the union that leaving without a deal could do.”

The Labour leader, Jeremy Corbyn, said: “The government has been defeated again by an enormous majority and it must accept its deal is clearly dead and does not have the support of this house.”

Moments after the crushing defeat, Donald Tusk, president of the European council, warned that he expected a “credible” reason for any delay to Brexit.

“Should there be a UK reasoned request for an extension, the EU27 will consider it and decide by unanimity,” a spokesman for Tusk said. “The EU27 will expect a credible justification for a possible extension and its duration.”

The ERG’s Steve Baker, together with the former education secretary Nicky Morgan and other senior Conservatives, quickly tabled an amendment to the government’s motion for Wednesday that would force May to pursue the so-called Malthouse compromise.

The government will publish fresh details of its no-deal policies, including tariffs on food imports and how it will handle checks at the Northern Ireland border, on Wednesday morning.

Philip Hammond, the chancellor, is also likely to underline the risks of no deal when he delivers his spring statement on Wednesday, before the debate.

Some members of the ERG – including the former foreign secretary Boris Johnson – claim a no-deal Brexit would be preferable to May’s deal, and hope it could still happen. He said the prime minister’s deal had “reached the end of the road”.

May insisted: “Voting against leaving without a deal, and for an extension, does not solve the problems we face. The EU will want to know what use we want to make of that extension. The house will have to answer that question.”

She declined to set out how she would allow parliament to make that decision. But the motions on Wednesday and Thursday will be amendable, potentially allowing MPs to put forward their own alternatives.

MPs pressing for a softer Brexit have signalled that they are ready to push the government to allow a series of votes to identify where a cross-party majority could be found – and believe they have supporters inside government.

The former Tory minister Nick Boles warned his Brexiter colleagues even before Tuesday’s vote that he and his allies would “do whatever it takes to frustrate you”, and “work with opposition parties to build a majority for a softer Brexit deal”.

Nick Boles MP (@NickBoles) We will then do whatever it takes to frustrate you. We will vote to stop no-deal Brexit on 29th March. We will vote to extend Article 50 for a few months. And we will then work with opposition parties to build a majority for a softer Brexit deal.

But senior Tory insiders suggested May could instead attempt to bring her deal back a third time, in what is already being dubbed “meaningful vote 3”.

Late on Tuesday night, May’s spokesman declined to rule out the idea of the PM putting her vote to parliament yet again, despite having already suffered two of the four biggest ever parliamentary defeats in the past 100 years.

“She said at the beginning that she believes very strongly that the House of Commons wants to leave with a deal, and she very strongly believes that the deal she has negotiated is the best deal which is on offer,” he said. “But parliament over the next two days now potentially has two very significant decisions to make.”

He also denied swirling rumours at Westminster that May could ultimately be forced to call a general election to overcome the stalemate in parliament. “We are not preparing for, we do not want a general election: our position is unchanged,” he said.

May’s defeat came despite her late-night dash to Strasbourg on Monday, during which Jean-Claude Juncker signed off on three additions to the agreement struck in November.

These included a joint interpretative instrument fleshing out both sides’ obligations to negotiate in good faith, a joint statement that they would work on alternative arrangements, and a unilateral statement by the UK that there would be nothing to stop Britain seeking to “disapply” the backstop if negotiations broke down.

Earlier, the attorney general, Geoffrey Cox, had called on his colleagues to treat the vote as a “political judgment”, after his legal advice offered little comfort to those concerned about the backstop.

In his statement, he suggested the changes reduced the risk of the UK being trapped indefinitely in the Northern Ireland backstop – but did not eliminate it.