New Delhi, June 19 -- Keir Starmer isn't on the ballot, but the U.K. prime minister's future is on the line in a special election on Thursday.

Voters in the Makerfield district of northwest England are electing a new lawmaker, and the leading contender is Andy Burnham of the governing Labour Party, the current mayor of Greater Manchester and oddsmakers' favorite to be the next prime minister.

If Burnham defeats a candidate from the anti-immigration party Reform UK and wins the seat for Labour, he's almost certain to challenge the embattled Starmer for leadership of the party, and the country.

Burnham has pledged that "if people put their trust in me, I will change politics" - a big promise for a politician who, if he wins, will be just...