In normal times, five election-winning, center-left political leaders from around the world, gathered in an imposing marbled hall in London, would be a stirring show of strength for champions of liberal politics.

Instead, the prime ministers, who include Canada’s Mark Carney, Australia’s Anthony Albanese, and Britain’s Keir Starmer, are set to meet on Friday at a moment when their brand of progressive politics has rarely seemed more endangered.

Fickle voters, stagnant economies and a polarizing debate over immigration have left center-left governments vulnerable to right-wing populists. In the United States, the Democratic Party is limping in the political wilderness, unable, as yet, to formulate a persuasive message to counter President Trump.

Mr. Starmer, in a speech to the meeting, the Global Progress Action Summit, is expected to make an impassioned case for progressive politics in the face of a stiff challenge from Nigel Farage, whose anti-immigrant party, Reform U.K., holds almost a double-digit lead in polls over Mr. Starmer’s Labour Party.

With anxieties about immigration on the rise, the prime minister is expected to balance that message by announcing a compulsory digital ID plan, which proponents say would deter illegal migrant workers.