LONDON — He jabbed his finger in the air and shook his head theatrically. He dared the opposition to back his call for an election and sneered that the Labour Party’s leader was a “chlorinated chicken.”

By the time Prime Minister Boris Johnson finished taking questions in Parliament on Wednesday, he had ushered in a new season of political mayhem in Britain, one in which the voters are now as likely as their feuding leaders to resolve the questions over how and when Britain should leave the European Union.

The raucous spectacle in the House of Commons illustrated the obstacles Mr. Johnson will face as he tries to lead Britain out of the European Union next month. On Wednesday, Parliament handed the prime minister two stinging defeats.

It first blocked his plans to leave the union with or without an agreement. And it then stymied his bid, at least for the moment, to call an election for Oct. 15, out of fear he could secure a new majority in favor of breaking with Europe, deal or no deal.