Brexit has become the lens through which all politics is viewed in the United Kingdom, for better or worse. And that may be threatening public confidence in the country’s democratic institutions.

When the United Kingdom’s highest court ended the suspension of Parliament by Prime Minister Boris Johnson Tuesday, its landmark ruling barely mentioned Brexit. Indeed, in a strictly judicial sense, the Supreme Court decision was not about Brexit at all.

But the politics of the fitful effort to extract the U.K. from the European Union has heavily shaped how a divided and dug-in country received the court’s verdict.

Pro-Brexit campaigners lambasted the court as another establishment tool designed to thwart the 17.4 million people who voted to leave in 2016. Angry callers to radio stations invoked the “will of the people” against the court’s legitimacy and questioned the political neutrality of its 11 judges, who unanimously upheld a Scottish court decision that Mr. Johnson had failed to justify his decision last month to suspend Parliament for five weeks.

In the opposite camp, calls for Mr. Johnson to resign are growing and are set to heat up on Wednesday when Parliament returns to the fray. To critics of Brexit, the ruling reveals a cavalier and contemptuous government that is breaking democratic norms, all in the name of delivering on a referendum that was said to be about restoring British sovereignty.

Unlike its counterpart in the United States, the Supreme Court is a new and relatively untested institution, meant to be a check on the bedrock of British democracy: parliamentary sovereignty. That its procedural ruling is facing angry pushback from Brexit supporters, and only grudging consent from Mr. Johnson’s government, could be a sign of a rocky road ahead for it and other democratic institutions.

“Everybody is now seen as partisan in the Brexit process, that’s one of the dangerous and invidious effects of Brexit. It has undermined people’s faith in the institutions that are meant to guarantee law and order and fair play and due process,” says Steven Fielding, a professor of political history at the University of Nottingham in England.