“We’ve been lied to so many times, haven’t we?” said Steve Ridley, 60, as snooker balls cracked in the background and a bartender called out crossword hints.

Mr. Ridley, who imports motorcycle parts, predicted that a no-deal Brexit would mean “slightly more paperwork until we get it sorted,” but certainly nothing serious, and there was no one in the Hare and Hounds who disagreed. Darren Smith, on a stool behind Mr. Ridley, called the warnings “scaremongering.”

“If the government had come up with these facts and figures before, maybe I would believe them now,” said Mr. Smith, 47. “They gave us the vote to get out of Europe, and now they delay and delay. It’s just a farce. It’s all a farce. I don’t trust any of them.”

This is where Britain is, on the cusp of one of the largest policy choices in its history: Battered by three years of political opportunism and partisan debate, many voters have less and less trust in the country’s institutions.