Ms Truss picked up 15 votes to command the support of 86 Tory MPs in the penultimate ballot, as the right of the party appears to be coalescing around her in the race for No 10.
Ms Mordaunt increased her share by 10 to sit on 92, while Mr Sunak gained an extra three votes to put him in 118, just shy of the number effectively guaranteeing him entry to the final phase.
Ms Badenoch came last in the ballot on 59 votes, with Ms Truss believed to be more likely to pick up a significant number of those votes than Ms Mordaunt during the next ballot to be held on Wednesday.
Ms Truss, Britain’s foreign secretary, was the big winner on Tuesday, after 31 votes were freed up by the elimination of Tom Tugendhat a day earlier.
The momentum of her latest result now puts her favourite to face Mr Sunak in the head-to-head competition to win a ballot of Conservative members, with that result being announced on September 5.
Mr Sunak, the former British chancellor, received a blow in the latest limited polling of the party membership, which forecast he would lose against both of his remaining rivals in the run-off.
Ms Mordaunt, Britain’s trade minister, said: “We are so nearly across the finish line. I am raring to go and excited to put my case to members across the country and win.”
She thanked Ms Badenoch, the former equalities minister, and praised her “fresh thinking and bold policies” in a possible pitch to begin winning over her now-floating voters.
Mr Sunak’s campaign focused on polls showing that he could beat Labour leader Sir Keir Starmer and “is the candidate the public think would make the best PM”.
Who the Tory membership favours is hard to judge because of the low levels of participation in existing polling.
But a YouGov survey of 725 party members over Monday and Tuesday saw Mr Sunak losing against all of his remaining rivals by large margins.
The survey put Ms Truss beating Mr Sunak by 54 to 35 and Ms Mordaunt beating him 51 to 37.
Ms Mordaunt, who had been put ahead in recent weeks, was losing to both Ms Truss and Ms Badenoch in head-to-heads by narrow margins.
The current size of the Conservative membership is unknown, but at the last leadership election in 2019 there were around 160,000 members, and insiders expect it to have grown, meaning the polling is not representative of the party.
The Sunak, Truss and Mordaunt campaigns will now focus on trying to pick up Ms Badenoch’s supporters ahead of the final vote of MPs on Wednesday afternoon.
This afternoon colleagues once again put their trust in me and I cannot thank them enough. We are so nearly across the finish line. I am raring to go and excited to put my case to members across the country and win.
— Penny Mordaunt (@PennyMordaunt) July 19, 2022
Former Tugendhat backer Anne-Marie Trevelyan, Britain’s international trade secretary, came out in support of Ms Truss.
Ahead of Tuesday’s result:
– Mr Sunak promised harsher sentences for criminals who refuse to attend court for their sentencing hearings and a crackdown on grooming gangs.
– Ms Truss promised to increase defence spending by 2030 and strengthen the intelligence services.
– Ms Mordaunt used a Daily Telegraph article to promise she would ditch housing targets if she enters Downing Street, saying they have been “tested to destruction”.
– Boris Johnson used his final cabinet meeting as prime minister to say the net-zero policy to tackle climate change is the “right thing to do” even if it is “unfashionable”, after criticism from the leadership contenders.
Apologies for missing key vote.
Air travel chaos, after meet with the Moldova President, prevented return. Saddened to lose the whip.
I carry on – good to be in ODESA and meet the impressive Mil Governor Marchenko to seek ways of re-opening the port & get that vital grain out. pic.twitter.com/gOKJnazKQS
— Tobias Ellwood MP (@Tobias_Ellwood) July 19, 2022
– Senior backbencher Tobias Ellwood, a supporter of Ms Mordaunt, had the Tory whip removed after failing to back Mr Johnson in a confidence motion on Monday.
Meanwhile, Ms Mordaunt said she remains “committed” to Mr Johnson’s flagship levelling-up agenda amid concerns that the high-investment policy could be shelved for less costly policies once he leaves office in September.
British transport secretary Grant Shapps, who is backing Mr Sunak, insisted on LBC radio that the former chancellor is a “huge fan of levelling up”.