That would spell defeat for the government on Monday, when it will hold a second parliamentary vote on elections, adding to the prime minister’s troubles just as a bill averting a no-deal Brexit is set to become law.

The resulting chaos has left Britain’s government enfeebled, and its path to leaving the European Union more inscrutable than ever. Lawmakers are now demanding Mr. Cummings’s resignation. Protesters are waving placards with his visage, but embellished with small red horns. Rumors of his imminent firing are gaining traction in Westminster.

Mr. Cummings is said to be plotting a radical response, with Mr. Johnson preparing to defy the law averting a no-deal Brexit by refusing to ask Brussels for a delay, ministers said on Sunday. That could draw the courts into the dispute as the clock ticks down to Oct. 31., a spectacle that Mr. Cummings reckons will only burnish the prime minister’s credibility with pro-Brexit voters far from London.

But it could also drive more moderate voters from the Conservatives for decades. And British news reports said that even Mr. Johnson was concerned that the hardball tactics have backfired.

A serial provocateur, talented strategist and political assassin, Mr. Cummings has built his career on the outrage of the so-called blob, as he calls parts of the establishment. He has no known political affiliation, concentrating his energies on shaking up Britain’s political system.

“Dom has so far been very effective in running campaigns against things,” said David Laws, a former lawmaker from the Liberal Democrats who worked with Mr. Cummings in the Education Department. “Now we’ll see whether he can make the transition into government and create things, rather than smash them up.”