Rishi Sunak was seen as Boris Johnson’s likely successor. Then the campaign began.

CARDIFF, Wales — Earlier this summer, Rishi Sunak, the former chancellor of the Exchequer, seemed well-placed to become Britain’s next prime minister, topping the short list of two contenders selected by Conservative Party lawmakers to replace the departing Boris Johnson.

With an impeccable résumé, a reputation for competence and a reservoir of good will from having guided Britain’s economy through the pandemic, Mr. Sunak was regarded as perhaps the country’s brainiest, most polished and most successful frontline politician.

Yet opinion polls have consistently shown him trailing the foreign secretary, Liz Truss, in the race to succeed Mr. Johnson.

Mr. Johnson’s departure from Downing Street after a series of scandals has left the ultimate decision on his successor in the hands of around 160,000 Conservative Party members, a small “selectorate” that, by definition, is more right-wing than the general population but also whiter, older and more male.

Many remain loyal to Mr. Johnson, and that has also created a problem for Mr. Sunak: He has been accused of treachery by some Conservative Party members because his cabinet resignation helped set off the rebellion against the prime minister.

A politician unaccustomed to failure, Mr. Sunak, 42, was until recently the undisputed rising star of British politics. He is also a walking success story of multiracial Britain, having been born in Southampton, on the south coast, to parents of Indian heritage who settled in the country six decades ago. If he wins the election, Mr. Sunak would become Britain’s first prime minister of color.