Andy Burnham leads Polymarket pricing on the next UK prime minister in 2026 because Labour’s May local election losses have intensified pressure on Keir Starmer, positioning the Greater Manchester mayor as the strongest internal challenger. Burnham’s candidacy in the June 18 Makerfield by-election offers a direct route into Parliament and the 20 percent MP threshold needed to force a leadership contest. Traders price “no next PM in 2026” at 19 percent to reflect uncertainty over whether Starmer can survive until year-end or whether any contest produces a different winner. Secondary names such as Angela Rayner, Wes Streeting and Ed Miliband trail because they lack comparable national polling strength or an immediate parliamentary vehicle, while opposition figures remain marginal absent an early general election. The imminent by-election outcome and any subsequent leadership moves are the primary near-term catalysts.