In a significant move, the work and pensions secretary broke ranks with Conservative colleagues to say the matter should be returned to the British people if Theresa May's deal is voted down in a Commons showdown in the New Year.
Ms Rudd acknowledged her comments would “distress” some of her Conservative Party colleagues and stressed she was fully committed to the prime minister's plan.
However it was hailed as a “massive moment” by People’s Vote campaigners, with Tory former minister Anna Soubry praising Ms Rudd as “brave and principled”.
The Independent has won the backing of more than 1m people for its Final Say campaign, which is calling for a fresh referendum on the final Brexit deal.
Ms Rudd backed the idea of so-called indicative votes to find which Brexit options MPs would be prepared to support if the prime minister’s deal is rejected.
The work and pensions secretary told ITV’s Peston: “I don’t want a people’s vote, or a referendum in general, but if parliament absolutely failed to reach a consensus I could see there would be a plausible argument for it.”
She added: “Parliament has to reach a majority on how it’s going to leave the European Union. If it fails to do so, then I can see the argument for taking it back to the people again, much as it would distress many of my colleagues.”
Ms Rudd said an indicative vote would “flush out” MPs by forcing them to show their support for one option or another, and encourage those whose favoured ideas are rejected to reach a compromise.
“We are going to have to find a way, as MPs, of working together to find a consensus, of agreeing on how to stop no-deal taking place,” she said.
Her comments were seized on by pro-EU campaigners.
Labour’s Owen Smith, a backer of anti-Brexit group Best for Britain, said: “Amber Rudd may be the first Tory cabinet member to say she’d rather have a people’s vote than allow a catastrophic no-deal to unfold, but she won’t be the last. This is a massive moment for our campaign.”
Meanwhile Ireland followed the UK and the European Union in setting out the latest stages of its no-deal Brexit planning.
“In many significant ways, a no-deal Brexit would pose unique, unprecedented and extremely difficult challenges for the EU, including Ireland, and especially the UK,” the Irish government document said.
As part of the plan, Dublin Port is creating extra parking for hundreds of trucks from the UK awaiting inspection after Brexit.
In London, Ms May will meet her Polish counterpart Mateusz Morawiecki for talks.
The discussions are expected to focus on defence and security cooperation, but come as the prime minister is desperately trying to secure further reassurances from EU leaders about the Northern Ireland backstop measures in the Brexit deal before the crunch Commons vote in the week commencing 14 January.
Scotland’s first minister Nicola Sturgeon, who met the prime minister on Wednesday, said Ms May’s goals were “a wee bit nebulous”.
“There’s not a lot of detail there,” Ms Sturgeon said. ”She says she’s working with the EU, trying to find assurances. I pressed her to give a bit more detail on that. I have to say it wasn’t forthcoming.”
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