Another Brexit referendum will become a “plausible” way forward if there is deadlock in Parliament, Work and Pensions Secretary Amber Rudd has said.
She told ITV’s Peston show while she did not personally support another vote, the case for one would grow if MPs could not agree another solution.
She said she hoped MPs would back Theresa May’s deal with the EU next month but it would be “very difficult”.
The PM says the UK must be ready to leave without a deal if it is rejected.
Mrs May has repeatedly ruled out holding another referendum, saying it was the government’s duty to implement the result of the 2016 Brexit vote.
A Downing Street source said the government was “very clear we are 100% opposed” to another referendum.
The UK is due to leave the EU on 29 March 2019 but an agreement on the terms of its withdrawal and a declaration on future relations will only come into force if the UK and EU Parliaments approve it.
The Commons vote was due to be held earlier this month but the PM postponed it once it became clear it would be defeated by a large margin.
She has since sought to gain further assurances from EU leaders to allay MPs’ concerns.
Ms Rudd told Robert Peston she could not be sure MPs would back the deal. She suggested arguments for another referendum would come into play if they did not and if they rejected other options.
“I have said I don’t want a People’s Vote or referendum in general but if parliament absolutely failed to reach a consensus I could see there would be a plausible argument for it,” she said.
“Parliament has to reach a majority on how it is going to leave the EU. If it fails to do so, I can see the argument for taking it back to the people again as much as it would distress many of my colleagues.”
If Mrs May’s deal is rejected, the default position is for the UK to leave in March unless the government seeks to extend the Article 50 negotiating process or Parliament intervenes to stop it happening.
Ms Rudd, who has likened the idea of a no-deal exit to a car crash, said it was imperative that MPs “find a way of getting a deal through Parliament”.
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To that end, she said she backed the idea of testing the will of Parliament through a series of “indicative” votes on “Plan B” options should MPs reject the PM’s agreement.
“It would flush out where… the majority is,” she said. “So people who hold onto the idea of one option or another would see there is no majority and so they will need to move to their next preference.
“We will hopefully be able to find where the compromise and the consensus is.”
Speaking on the same programme, Labour’s shadow education secretary Angela Rayner said talk of another referendum was “hypothetical” at this stage and would represent a “failure” by Parliament.
She accused the prime minister of trying to scare MPs into backing her deal by delaying the vote on it to the latest possible date.
Earlier on Wednesday, the European Commission announced a series of temporary measures designed to reduce the economic impact if the UK was to leave without a comprehensive legally-binding agreement.
But it made clear that it could not counter all the problems it expects.
The Republic of Ireland has given more details of its own no-deal contingency planning, saying the risk of the UK leaving without an agreement was “very real”.
It warns of potentially “severe macroeconomic, trade and sectoral impacts” for Ireland as well as “significant gaps” in policing and judicial co-operation.
In such a scenario, it said its priorities would be to uphold the Common Travel Area between the UK and Ireland, ensure there is no return of physical checks on the border between the Republic and Northern Ireland and ensure the “best possible outcome” in terms of trade.
The UK has allocated a further £2bn in funding to government departments to prepare for the possibility and has urged businesses to put their own no-deal plans in motion.