Keir Starmer is not on the ballot, but the UK prime minister’s future is on the line in a special election on Thursday. Voters in the Makerfield district of northwest England were electing a new lawmaker, and the leading contender is Andy Burnham of the governing Labour Party, the current mayor of Greater Manchester and oddsmakers’ favourite 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 is almost certain...