LONDON — Conservative Party lawmakers in Britain are casting ballots Wednesday in the first round of an election to replace Prime Minister Johnson.

The internal party contest will replace a figure famous in Britain and around the world with a new and much less well-known prime minister.

Eight candidates have secured the required backing of 20 of their colleagues to make the first ballot. The 358 Tory legislators will vote Wednesday afternoon, with the last-placed candidate and any others who fail to get 30 votes dropping off the list. Further rounds of voting will take place Thursday and, if needed, next week.

The final two contenders will face a runoff vote by about 180,000 Conservative Party members across the country. The winner is scheduled to be announced September 5 and will automatically become prime minister, without the need for a national election.

Few of the contenders have a high public profile. The former Treasury chief, Rishi Sunak, is the bookmakers’ favorite and has the largest number of declared supporters, followed by Foreign Secretary Elizabeth Truss and the trade minister, Penny Mordaunt.

The current Treasury chief, Nadhim Zahawi; backbench lawmaker Tom Tugendhat; the ex-equalities minister, Olukemi Badenoch; the former foreign secretary Jeremy Hunt; and Attorney General Suella Braverman are also on the ballot.

The candidates are jostling to replace Mr. Johnson, who quit as Conservative leader last week amid a party revolt triggered by months of ethics scandals. He will remain in office as a caretaker prime minister until his replacement as party chief is chosen.

Ms. Mordaunt, at her official campaign launch on Wednesday, said the party had “standards and trust to restore” after the scandal-tarnished Mr. Johnson years.

She said voters “are fed up with us not delivering, they are fed up with unfulfilled promises and they are fed up with divisive politics.”

The slate of candidates is strikingly diverse, with four contenders from ethnic minorities and four women. But all are offering similar tax-slashing pledges, with only Mr. Sunak offering a note of caution. 

He has cast himself as the candidate of fiscal probity, saying the country needs “honesty and responsibility, not fairy tales” to get through economic shock waves from the coronavirus pandemic and the war in Ukraine.