LONDON — Britain’s opposition Labour Party said on Monday that it was prepared to support a second referendum on withdrawal from the European Union, a shift that could have significant ramifications for the fate of Brexit and for the country’s future.

After the resignations of nine Labour Party members last week, and amid the prospect of more, the party’s leader, Jeremy Corbyn, dropped his longstanding resistance to a second vote on leaving the bloc.

Mr. Corbyn’s support for a new vote is certainly no guarantee a new vote will happen. Still, it will cheer pro-European Britons, who have been fighting to reverse the outcome of the 2016 referendum decision.

The Labour statement on Monday was lacking in detail, and it was not immediately clear when the amendment for a second vote would be put forward in Parliament and what question, exactly, it proposed to put to the people.