LIVERPOOL, England — Jackie Walker, a prominent left-wing activist, was in full flow. “We’re part of the biggest political moment in the last 50 years!” she cried. “The seeds we are sowing, who knows what fruit they will bring?”

The packed audience in a former Congregational chapel turned arts center here cheered with the fervor of a religious gathering, reflecting a kind of reverence for the man they had shown up to support: Jeremy Corbyn, the hard-left leader of Britain’s Labour Party. At the party conference in Liverpool just minutes away, he had defeated what his supporters called a “coup attempt” by more centrist Labour members of Parliament.

Many Labour legislators fear that Mr. Corbyn, 67, is dragging the party so far from the political and ideological mainstream that he will lead it to another devastating political defeat at the hands of the Conservative Party in the next general election, which is not due until 2020 but is possible earlier.

Despite Labour’s significant growth in grass-roots members, some fear successive defeats. Janan Ganesh, a Financial Times columnist, wrote that “there is a reasonable chance, and it becomes stronger by the day, that Gordon Brown will turn out to have been the last Labour prime minister.” (Mr. Brown left office in 2010.)