Theresa May’s plans to get her Brexit deal through parliament ran into fresh difficulties on Friday as it emerged that a “no to no deal” amendment submitted by Labour’s Hilary Benn with the support of two Tories had won the backing of the SNP and Lib Dems.

Joanna Cherry, an SNP frontbench MP, said her party’s 35 MPs would support Benn’s “excellent” amendment, which rejects both May’s deal and a no-deal Brexit and gives parliament a say in what the government would do next.

The Lib Dems also said they would give their support, alongside Labour and the Tory rebels who declared their backing on Thursday, meaning that it has a chance of success if the other minor parties and a dozen or so more Conservatives follow suit.

Benn said his amendment declined to approve May’s deal, rejected the UK leaving the European Union without a deal, and “enables parliament to express a view, to see if there was an alternative that could get support”.

The current legislation means that if May’s deal is rejected on 11 December, the government must make a statement within 21 days to say what it will do in the light of the defeat. That would present a serious blow to the prime minister, although she could in theory return with essentially the same deal and put it to the house again.

But if ministers were to propose a no-deal Brexit, the existing rules make it difficult for MPs to overturn that because the legislation only provides for parliament to note the government’s decision at that point.

MPs who support a hard Brexit are planning to simply vote against May’s final deal, once all the amendments have been dealt with – but the consequences of that make an economically damaging no-deal scenario more likely.

Benn hopes his amendment would allow MPs who might otherwise have supported the prime minister because they are concerned about the risks of crashing out of the EU without a deal to vote against May’s Brexit plan.

An estimated 94 Conservative MPs have said they will vote down May’s final deal, but the prime minister insisted that she was pressing ahead with the vote regardless.

“When it comes to the vote that people are being asked to make in the House of Commons, I think we should remember that we gave the vote to the British people as to whether or not to leave the EU,” May said in an interview with the BBC during her trip to the G20 in Argentina.

When pressed, the prime minister would not rule out trying to stage a second vote shortly to try and win approval at the second time of asking. “I’m focused on the vote that is taking place on December 11 and I want everybody who is going to participate, all the MPs, to focus on what this vote does,” she added.

May also avoided answering whether she would be prime minister in a fortnight if she were defeated. “What I’m doing is focusing on that vote because this is not about me or any individual member of parliament,” she said and called on every MP to put the national interest first.

No 10 sources denied they would consider pulling the vote in the middle of the debate in an attempt to see if they could wring additional concessions out of the EU, before bringing it back to parliament.

There had been speculation at Westminster that the idea was being considered by the whips’ office but insiders said that the message to MPs was that the vote on 11 December was final and that the alternative was no deal, or possibly no Brexit.

Liam Fox, the trade secretary and one of the cabinet’s senior Brexiters, urged MPs to get behind May’s deal, saying that MPs were voting on the legally binding withdrawal agreement the week after next – but that the future trading relationship between the UK and the EU remained up for grabs.

He said: “Whatever deal we want to have in future still requires a withdrawal agreement. This is something people don’t seem to be grasping. Whether it’s the deal that the prime minister has set out for leaving the EU, or the Norway style, or the Canada plus FTA, they still require the withdrawal agreement.”

Benn’s amendment was one of five submitted on Thursday, but appears to be the one most likely to cause serious difficulties for May. A Labour frontbench amendment rejecting May’s deal submitted by Jeremy Corbyn was announced earlier this week – but it is unlikely to attract any Conservative support.

Three backbenchers, the Conservatives Sir Edward Leigh and Giles Watling, plus independent former Labour MP Frank Field, also put down amendments that try to neutralise the Northern Irish backstop, amid concern that it could be used by the EU to trap the UK in an indefinite customs union.