Keir Starmer, the party's Brexit spokesman, used a speech Saturday to say that it is now up to Parliament to take the tough decisions needed to break the Brexit impasse. He said holding a second referendum on Britain's EU membership has to remain an option.
May's Brexit withdrawal plan from the EU was soundly rejected in Parliament this week, leading to crisis talks with other parties before her return to Parliament on Monday with an amended Brexit plan.
Britain is scheduled to leave the bloc on March 29 and so far does not have a Parliament-approved withdrawal plan. Many economists warn this "no-deal" scenario could have serious economic consequences.
Austrian Chancellor Sebastian Kurz suggested Saturday the EU may be willing to give Britain more time to leave if it has a good strategy because a "no-deal" departure would be bad for everyone. He was quoted by Germany's Welt am Sonntag newspaper as saying "if London presents an orderly strategy and plan, a postponement of the exit date by a couple of months is conceivable."
He said: "One thing is certain: a hard, disorderly Brexit would harm us all."
Cross-party talks in Britain designed to move the Brexit process forward have so far failed to produce momentum toward a solution.
Labour Party leader Jeremy Corbyn refuses to take part in the talks May has requested until she removes the possibility of a "no-deal" departure from the table. She says there is no legal way for her to do so.
Corbyn said in a Friday night letter to May that the talks are just a delaying tactic and complained that she is unwilling to consider extending the deadline for Britain's withdrawal or allowing a second Brexit referendum.
Former Conservative Prime Minister John Major told the BBC on Saturday that a "no-deal" departure would be the worst possible outcome, one that would harm millions.
He said Parliament should be allowed to hold a series of "indicative" votes on a number of different Brexit plans and lawmakers should vote without being constrained by party loyalties. He says a second referendum may be necessary now that the complexity of Brexit is better understood.
David Rising in Berlin contributed.
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