Ms Mordaunt, who had a 17-point lead over Sunak last Tuesday, outscored the former chancellor by two points in the most recent data, 41% from 43% in a second round.
The Minister of International Trade had been 18 percentage points ahead of Truss, but the Foreign Minister has opened up a seven-point lead from 48% to 41%.
Last week, a separate investigation by ConservativeHome and YouGov showed that Mrs Mordaunt was the election of Conservative members for the next Prime Minister, but has now been overthrown by Mrs Badenoch and also overthrown by Mrs Truss.
Ms. Badenoch’s supporters also hope that the friendship between her and Mr. Tugendhat will lead her to get her personal support.
“There’s no good reason why Tom can’t endorse Kemi,” one supporter said. “Kemi is a good friend of Tom: they have a close personal relationship.”
The separate survey by Bradshaw Advisory, a political consultancy, published Sunday, found that Ms. Badenoch outperformed Mr. Tugendhat in several categories about which conservative voters were asked, including charismatic, determined and resembling someone for whom he would vote.