Rishi Sunak wanted to show strength last week as he claimed victory on his pledge to clear the backlog of U.K. asylum cases. Instead, the prime minister underscored what allies fear is a growing political weakness.

The British prime minister took office in late 2022 promising to govern with "integrity, professionalism and accountability” — an attempt to distance himself from his two predecessors, Boris Johnson and Liz Truss. Five targets announced 12 months ago, ranging from the economy to immigration and the National Health Service, would give voters a transparent way to judge him, he said.

But the strategy is unraveling as Sunak tries to bank credit for what he says is delivering on the goals. The prime minister is finding out, via his slumping approval ratings, that meeting targets that are far more narrowly defined than the way he presented them to voters is not working for him.