LONDON — Prime Minister Theresa May returned from a seemingly unproductive meeting with European Union leaders to a growing attempt by British lawmakers to stop her from taking Britain out of the EU on March 29 without a divorce deal.

With May and the EU at odds over not just how, but when Brexit should happen, her political opponents were getting increasingly desperate to take control of Britain’s muddled departure from the bloc.

At an EU-Arab League summit in Egypt, the EU warned Britain it faces the prospect of delaying its planned March 29 departure or the consequences of a chaotic exit. European Council President Donald Tusk, who chairs meetings of EU nation leaders, said Monday it would be “rational” to postpone Brexit day.

May insisted she intends for Britain to leave as planned. But her often divided opponents may be coalescing around a plan to prevent Britain crashing out of the EU with no agreement in place.

The main opposition Labour Party took a big step Monday toward backing a new referendum on the country’s EU membership.

The party has previously said it would support a referendum as a last resort if it could not secure a new election or make changes to May’s EU divorce deal. Britain’s Parliament has so far rejected the deal struck between May’s government and the bloc, and is due to hold a series of votes Wednesday on next steps in the Brexit process.

Labour has proposed its own withdrawal plan as an alternative to the government’s deal with the EU. The party said Monday it would back a second public vote if the House of Commons rejects its plan this week, as is widely expected.

Labour leader Jeremy Corbyn said the party is committed to “putting forward or supporting an amendment in favor of a public vote to prevent a damaging Tory Brexit being forced on the country.”

The party did not specify what voters might be asked to consider in any future vote, though it has previously said the option of Britain remaining an EU member would be included.

Labour has previously said it would only support a second referendum as a last resort if it could not secure a new general election or make changes to May’s divorce deal.

The change in approach follows the resignations of nine Labour lawmakers last week, partly over the party’s failure to back another Brexit referendum. It is likely to cheer many party members, who have backed calls for a so-called “people’s vote.”

The path to another Brexit vote is far from clear. It would require the support of numerous lawmakers from the Conservative Party.