BRIGHTON, England — Jeremy Corbyn, the leader of Britain’s opposition Labour Party, told supporters on Wednesday that their brand of left-wing politics had brought them to “the threshold of power,” as he ended an annual conference that consolidated his grip over the party and marked another stage in his journey from fringe politician to potential prime minister.

In a speech of around 80 minutes, Mr. Corbyn mocked his detractors, including Prime Minister Theresa May, and criticized President Trump, winning frequent applause from party members who have been buoyed by Labour’s performance in elections in June, which exceeded most expectations and deprived Mrs. May and her Conservative Party of a parliamentary majority.

The four-day meeting, in the seaside city of Brighton, underscored Labour’s shift to the left, focused in large part around Mr. Corbyn, who was once seen by many in his party as an electoral liability.

In some respects a British version of Bernie Sanders, Mr. Corbyn, 68, has championed an agenda that includes nationalizing utilities, abolishing university tuition fees and increasing taxes for the wealthy and for corporations.