The leader of the Liberal Democrats, Jo Swinson, has reiterated that she would work with the Labour party to prevent a no-deal Brexit amid pressure from other opposition leaders, but underlined her belief that a Jeremy Corbyn-led unity government would not win the confidence of the House of Commons.

The Conservative grandee Ken Clarke and senior Labour MP Harriet Harman – the father and mother of the house – are prepared to lead the emergency government, Swinson added, saying she had won both of their assurances.

“I have been in touch with them because obviously you don’t just mention people’s names without checking that they’re OK with that,” Swinson told BBC Radio 4’s Today programme on Friday.

“They put public duty first, and they don’t want to see a no-deal Brexit, and if the House of Commons asks them to lead an emergency government to get our country out of this Brexit mess and to stop us driving off that cliff to a no deal, then yes, they are prepared to do that and I think that is to their credit.”

Her comments follow a letter that Corbyn sent to leaders of the Scottish National party, Plaid Cymru, the Green party and Tory rebels, outlining his plan to oust the government through a vote of no confidence and form a “strictly time-limited”, caretaker government to prevent a no-deal Brexit.

Swinson was quick to dismiss the idea on Wednesday, calling it “a nonsense”, but on Thursday evening she wrote to the Labour leader to discuss how the two parties might work together after coming under pressure from other opposition leaders including the SNP leader, Nicola Sturgeon.

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“I’ve always said I wanted to talk to him about it, and I think that dialogue is really important between anyone who wants to stop a no-deal Brexit,” she told Today.

“I think we have to focus on how we can actually succeed in stopping no deal because the clock is ticking. And I think it is good to talk to other parties – and I’m doing that, I’ve been doing that all summer and, obviously, just before the House of Commons rose for the recess I encouraged Jeremy Corbyn to table a vote of no confidence, which he didn’t do.”

The SNP, Plaid Cymru and Tory MP Guto Bebb have all signalled they could support the plan. Three Conservatives – Dominic Grieve, Oliver Letwin and Caroline Spelman – plus Nick Boles, a former Tory who is now independent, on Thursday agreed to meet Corbyn to discuss possible ways to block no deal.

Play Video 1:41 Jo Swinson says Corbyn cannot become temporary PM – video

But Swinson suggested that other senior MPs, such as Harman or Clarke, would be more likely to command support in the House. She said the proposal to legislate for a further extension of article 50 would be more viable than a Corbyn-led caretaker government.

“I want to deliver us staying in the European Union, I want to stop Brexit and I recognise that what we need to do with immediate urgency is stopping a no-deal Brexit.

“But people in No 10 – Dominic Cummings, Boris Johnson – they will be rubbing their hands that that we are talking about a plan here that has no chance of success,” she said.

The energy minister, Kwasi Kwarteng, said he thought it would be “an odd thing” for Clarke to take the helm at the age of 79. “I’m 44 years old. He was an MP before I was born. He’s been around for a long time,” Kwarteng told Today.

“I think it would be an odd thing for him to lead a unity government, you know. I think he’s nearly 80.”