The leadership race of Britain's ruling Conservative Party has been whittled down to three candidates, with former finance minister Rishi Sunak winning the most support in the fourth round of the vote.

Tory lower house members cast ballots in the fourth round on Tuesday to choose the successor to Prime Minister Boris Johnson.

Sunak garnered 118 votes, finishing in top place as he did in the past three voting rounds.

Junior trade minister Penny Mordaunt won 92 votes, followed by Foreign Secretary Liz Truss with 86 votes.

Former equalities minister Kemi Badenoch, who earned 59 votes, was eliminated from the race.

The three candidates will move to the fifth round which will take place on Wednesday to select the final two candidates. The big question now is who will pick up the votes of Badenoch's supporters.

The final two will campaign for about six weeks before some 200,000 members of the party across the country cast final ballots, with voting due to close on September 2. A winner will be announced on September 5.