LONDON — Back in the Obama years, when a recalcitrant Congress was obstructing any major piece of legislation the president put forward, his adviser David Axelrod used to look envyingly across the pond at his British counterparts, who seemed to find it so easy to get things done.

“We used to sit in the White House thinking it would be great to have a parliamentary system, where you’re guaranteed to rule with your allies,” he said.

Then he laughed. “It doesn’t look very appealing now.”

On Wednesday, the authority of Britain’s executive branch was diminished to a point not seen in recent history. The country watched an increasingly empowered group of backbench legislators take control of the government’s principal piece of legislation on the country’s exit from the European Union, suddenly altering the negotiating strategy sustained for more than two years by Prime Minister Theresa May.

No more can Britain boast about its streamlined, predictable “Westminster model,” in which a strong executive presides over a unitary state.