As internal pressure builds from some of her colleagues for Mrs May to ditch her Chequers Plan in favour of a Canada-plus trade deal, Amber Rudd, the former Home Secretary, laid bare the problems facing the PM in trying to unite her party.
He said: "That must include campaigning for a public vote".
It contracted earlier comments by Shadow Chancellor John McDonnell, and went against the strong opposition to staying in the European Union from Unite general secretary Len McCluskey.
Corbyn, a long-time euroskeptic, must find a way to reconcile his pro-EU MPs and members with the party's working class voter base, many of whom support Brexit, if he is to capitalize on May's vulnerability.
"I don't know whether Article 50 will have to be extended or not", he said.
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In a challenge to Brexit hardliners, she insisted that leaving the bloc without a deal was preferable to the Canada-style free-trade agreement, which they favor as it would unequivocally put the country outside customs union and single market.
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Even if May is able to secure a deal on Brexit with Brussels, it is far from certain she will be able to get the terms approved by parliament. Together Labour can stop the Tory hard Brexit.
Both Sir Keir and shadow foreign secretary Emily Thornberry told the conference that they would personally vote Remain in any re-run referendum.
"No deal would be a catastrophe and no government has the right to plunge our country into chaos due to their own failures", he said. "I doubt that very much and so do most people".
"And, frankly, this idea that we might have medicines stockpiled for six weeks has spooked people".
"Of course, to a significant extent, this also depends on what Britain really wants - the discussion isn't so clear here", she said.
Delegates at the party conference in Liverpool, northwest England, voted overwhelmingly for a motion that calls for a second referendum in the event that Parliament fails to approve an eventual deal. "So if the people's party decide they want the people to have a final say on the deal, we have to respect the view of our members and we will go out and argue for it".