Education Secretary Damian Hinds told the BBC a second referendum would not end the deadlock over Brexit but might simply extend the impasse.
Britain's government is not preparing for a second referendum on Brexit, ministers say, sticking to the script that Prime Minister Theresa May's deal could still pass through parliament with a few changes. "We've had the people's vote, we've had the referendum and now we've got to get on with implementing it".
But EU leaders told her the negotiated withdrawal agreement was "not open for renegotiation", although some clarification was possible.
Contingency planning for a "no-deal" Brexit has been stepped up, but May's office dismissed as "categorically untrue" a report in the Sunday Times that people would be warned not to book holidays after March.
Former British prime minister Tony Blair
She faces growing cabinet demands to allow parliament to shape the options through a series of non-binding free votes, with the education secretary, Damian Hinds, and the worldwide trade secretary, Liam Fox, indicating on Sunday they could back this. They include former leader Tony Blair, a long-time critic of Corbyn and a hugely divisive figure for Labour voters.
The British Parliament was supposed to vote on Ms May's Brexit plan last week, but she postponed it after it became clear that lawmakers would decisively reject it.
The move comes after close allies of Mrs May distanced themselves from reports that they were manoeuvring to bring about a fresh referendum.
"A new public vote would be different from the referendum in 2016 because we now know more about what Brexit means", said Margaret Beckett, an MP from the main opposition Labour Party and "People's Vote" supporter.
He said that would take some time.
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On Sunday, he said in a statement it would be "the sensible thing" to allow parliament to vote on each of the forms of Brexit canvassed, including the deal May agreed with the EU.
Fox said on BBC One's Andrew Marr Show: "Personally, I wouldn't have a huge problem with parliament as a whole having a say on what the options were".
May will urge MPs on Monday not to "break faith with the British people" by demanding a second referendum and will make a statement in the Parliament on last week's European council summit.
But Labour and other opposition parties, as well as some Tory Brexiteers say a decision is needed now, so alternative options can be considered if Mrs May's deal is rejected.
She will warn that another referendum would also "further divide our country at the very moment we should be working to unite it".
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While some senior cabinet figures believe a second referendum may be the only way out of the impasse to prevent the United Kingdom crashing out of the European Union without a deal on March 29, they believe that all other options must be tested first.
May then travelled to Brussels, seeking "legal and political assurances" over the Irish backstop to try to win over MPs at home.
Hinds is said to have proposed the idea in a cabinet conference call with May a week ago and was backed by fellow Remain-supporting ministers, including the Chancellor Philip Hammond, business secretary Greg Clark and work and pensions secretary Amber Rudd.
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