WOLVERHAMPTON, England — To understand the contradictions that are tearing the Labour Party apart, consider Ruth Wilkinson and Philip Handley, both Labour supporters. Ms. Wilkinson, 24, voted for Britain to remain in the European Union. Mr. Handley, 60, to leave.

The only bond that unites them is their fury at Jeremy Corbyn, the Labour leader, and his handling of the opposition to the government’s plan for Britain’s departure from the European Union, known as Brexit. Both are ready to ditch the party altogether.

“I’m absolutely devastated about the direction we’re traveling in,” Ms. Wilkinson, who works for a charity, said. “The party that I hold dear, and the party that I would stand behind, is not doing anything to offer a solution or an alternative.”

Mr. Handley said Labour had misled people like him.

“I’ve always voted for the Labour Party,” said the retired transport manager, who would prefer that Britain leave the bloc with no deal. “But this is the only thing I disagree with Jeremy Corbyn — how he handles Brexit.”