MPs backing a soft Brexit turned their fury on second referendum campaigners on Monday night, blaming MPs backing a people’s vote for parliament’s failure to reach a consensus.

The former chancellor Ken Clarke said second referendum campaigners had scuppered the chances of his motion on a customs union, which lost by just three votes. Clarke rejected the suggestion from the Green party’s Caroline Lucas that a compromise motion of a customs union and a referendum would win support.

“If you add the people’s vote to a motion like mine, you lose votes all over the place … vote for something you have no objection to as a fallback position,” he said.

Referendum supporters immediately hit back at the criticism, pointing out that the vast majority of MPs had compromised and that at least four were absent for personal reasons.

“Cooperation is needed, not competition, at this stage – and all of us fighting against a no-deal Brexit made that clear before these crucial votes,” one senior Labour MP said. “Parliament has come closer to a solution in seven hours than the PM has in two years.”

Key backers of a second referendum, including the Independent Group (TIG), Liberal Democrats, and Labour referendum supporters such as Jo Stevens and Owen Smith, voted against Clarke’s motion, which was also opposed by Labour leave supporters. The SNP instructed its 35 MPs to abstain.

The Lib Dem Norman Lamb, who had urged his party to back a compromise, said he was furious with the result. “I am so deeply distressed. I am ashamed to be a member of this parliament,” he said. “We have failed in our responsibility today. There has been far too much posturing and intransigence, including from my own party.”

Lamb said he believed the lack of compromise had pushed the UK closer to a no-deal exit. “It may now be too late,” he said. “I don’t hold out much hope now. There is a very real chance we will crash out. We have failed twice now and failed because of people who broadly support a customs union not being willing to back it.”

Stephen Kinnock, one of the key campaigners with Nick Boles for the common market 2.0 plan, or Norway-style Brexit, said he had been prepared to compromise by voting for the second referendum option. “It was therefore very disappointing to see that 33 colleagues who are campaigning for a referendum chose not to reciprocate,” he said. “It appears that some of us were acting in good faith and in a spirit of compromise whilst others were not.”

TIG’s Anna Soubry said backers of a referendum had also tried to forge a compromise with soft Brexiters, but any efforts to draft a composite motion had been rejected.

Soubry said she still hoped that a compromise to pair a soft Brexit with a referendum could be reached. “There is a way of getting this together. If you look at the figures, there is every chance on Wednesday we can find a compromise,” she said.

Days of intensive horse-trading in parliament convinced the Labour front bench and the Scottish National party to back common market 2.0.

Yet the motion still failed to reach a majority by 21 votes, coming behind a second referendum and a customs union, a motion that fell by just three votes. After the result, Boles resigned on the floor of the House of Commons, blaming his failure to convince his own party to compromise.

Play Video 0:57 Nick Boles: Tory MP resigns due to party’s unwillingness to compromise – video

Brexit: Labour to back common market 2.0/Norway amendment for staying in single market – live news Read more

Supporters of a soft Brexit or a second referendum acknowledged during the course of the day that they had not managed to convince anything like sufficient numbers of Conservatives to back a compromise option, with insufficient support for a stable majority to pass legislation for any compromise.

One significant intervention came on Monday afternoon. The Tory MP Huw Merriman, a parliamentary aide to the chancellor, Philip Hammond, wrote a letter to all MPs on Monday urging them to back the Peter Kyle motion for a referendum, saying he had got to the point where he believed it was preferable to a customs union.

“If, like me, you are not a supporter of this option, then I am appealing to you to consider the confirmatory vote option,” he wrote, though he said he sympathised with a constituent who compared the choice to “asking which leg he would like amputated”.

Q&A What is a customs union? Show Hide A customs union means that countries agree to apply no or very low tariffs to goods sold between them, and to collectively apply the same tariffs to imported goods from the rest of the world. International trade deals are then negotiated by the bloc as a whole. For the EU, this means deals are negotiated by by Brussels, although individual member state governments agree the mandate and approve the final deal. The EU has trade deals covering 69 countries, including Canada and South Korea, which the UK has been attempting to roll over into post-Brexit bilateral agreements. Proponents of an independent UK trade policy outside the EU customs union say Britain must forge its own deals if it is to take advantage of the world’s fastest-growing economies. However they have never explained why Germany manages to export more than three times the value in goods to China than Britain does, while also being in the EU customs union. Jennifer Rankin

Fifteen Tory MPs backed the motion for a second referendum. However, some MPs fear that Tories sympathetic to a second referendum have been spooked by the treatment of Dominic Grieve, the former attorney general who backed a fresh public vote and lost a vote of no confidence at an angry local association meeting last week.

“Tories saw the video of that meeting and are now thinking, ‘I don’t want any of that,’” one People’s Vote source said.

MPs still believe Clarke’s motion for a customs union has a high chance of success should MPs bring back another round of indicative votes on Wednesday.

However, the Labour MP Clive Lewis, a backer of a second referendum, said the cross-party coalition in favour of a softer Brexit would not hold for binding votes. “Although a customs union and common market 2.0 did well, they did so with the votes of MPs like me who would only support them in binding votes if they were then put to the people,” he said.