LONDON — Britain’s opposition Labour Party, already reeling after voters defied its advice and chose to leave the European Union, was plunged further into crisis on Tuesday when its leader, Jeremy Corbyn, overwhelmingly lost a no-confidence motion among his fellow lawmakers.

The measure, which passed by a vote of 172 to 40, opens the way for a challenge to Mr. Corbyn’s leadership. It technically changes nothing, as Mr. Corbyn has refused to step down, though it underscores his loss of authority among colleagues in Parliament.

“I was democratically elected leader of our party for a new kind of politics by 60 percent of Labour members and supporters, and I will not betray them by resigning,” Mr. Corbyn said after the vote by Labour members of Parliament. “Today’s vote by M.P.s has no constitutional legitimacy.”

He added: “We are a democratic party with a clear constitution. Our people need Labour Party members, trade unionists and M.P.s to unite behind my leadership at a critical time for our country.”