LONDON — Having twice thrown out Prime Minister Theresa May’s plan for Britain’s withdrawal from the European Union, the fractious British Parliament defied her again on Wednesday, worsening the power vacuum atop British politics just 16 days before the exit is scheduled to take place.

Parliament voted to oppose the prospect of a disorderly “no-deal” exit from the bloc, doing it in a dramatic and unexpected fashion that undercut the already-battered Mrs. May’s dwindling authority and negotiating leverage.

And the breakdown of discipline in her own Conservative Party renewed speculation that her own cabinet could try to force her from power.

No other prime minister in recent British history has been so unable, repeatedly, to work her will in Parliament. Nor have the backbench members of a ruling party felt so free to rebel openly against their leader.