LONDON — For the ever-wary lawmakers who sit behind Prime Minister Boris Johnson in Britain’s House of Commons, one insurance policy on his rollicking leadership was not enough. So on Saturday, they took out another.

So distrustful have lawmakers become of their famously brazen prime minister — and of one another — that they voted on Saturday not to vote at all on Mr. Johnson’s much-heralded Brexit plan.

They had already passed a law to prevent the prime minister from abruptly pulling Britain out of the European Union without a deal managing future relations. But on Saturday they went further, saying that even the deal that Mr. Johnson had struck with the European Union was not a strong enough guarantee that Britain would not leave without one.

So they bought themselves a second layer of protection against such an outcome, forcing the government to ask for an extension and putting off the fateful decision on his deal until a no-deal departure was a more remote possibility.