Rishi Sunak’s attempt to derail Liz Truss’s Tory leadership bid appeared to have failed on Tuesday, as a new opinion poll found that Conservative members believed that she won a crucial head-to-head televised debate.

The YouGov survey found Tory activists — who have the final say on who will be Britain’s next prime minister — thought Truss, foreign secretary, performed better than Sunak, ex-chancellor, by a margin of 50 per cent to 39 per cent.

The poll confirmed an earlier survey by Opinium which found that while ordinary voters thought Sunak had narrowly edged the BBC1 Tory leadership debate by 39 per cent to 38 per cent, Conservative supporters preferred Truss by 47 per cent to 38 per cent.

Sunak had sought to destabilise Truss, the bookmakers’ favourite, by strongly attacking her on tax and the economy, and repeatedly interrupting her. Thérèse Coffey, work and pensions secretary and a Truss supporter, accused the former chancellor of “mansplaining”.

Simon Clarke, Treasury chief secretary and also a Truss backer, accused Sunak of conducting himself in an “extremely aggressive” manner during the debate.

Clarke said on LBC he had always found Sunak to be “reasonable to work with” in the Treasury, but added his former colleague took a “pretty intense approach” during the debate.

Sunak said Truss’s plans to cut taxes would plunge “millions of people into misery” because it would prompt a sharp rise in interest rates and crash the economy.

Truss said Sunak had pursued “negative, declinist policies” and the tax increases he introduced as chancellor would plunge the UK into recession.

Following the debate, Truss’s spokesperson accused Sunak of “shouty private school behaviour”. One Truss campaign official said the former chancellor “totally lost his rag and showed how rattled he was”.

Sunak’s allies insisted that he was just showing how “passionate he is about the economic situation facing the country” and wanted to expose the dangers posed by Truss’s tax plans.

Former cabinet minister David Davis defended the former chancellor’s conduct, saying “fierce exchanges” and interruptions were part and parcel of political debate.

But time is running out for Sunak to win over the Tory party membership: more than 150,000 activists will receive ballot papers next week, with a new Conservative leader and prime minister due to be announced on September 5.

Polls suggest Sunak is trailing Truss in the contest, partly because Tory members blame him for putting up taxes to stabilise the public finances after the Covid-19 crisis but also due to his perceived disloyalty to Boris Johnson.

He was one of the first ministers to quit that forced Johnson’s resignation as Conservative leader.

The YouGov survey of Tory members confirmed Sunak’s problem. It found that Truss was ahead of Sunak by 63 per cent to 19 per cent when it came to being “in touch with ordinary people”.

The foreign secretary was also deemed to be more likeable by 54 per cent to 35 per cent, and trustworthy by 51 per cent to 37 per cent, while Sunak was narrowly ahead by 43 per cent to 42 per cent on the question of who seemed most “prime ministerial”.

Sunak now faces a dilemma ahead of further TV debates and Tory party hustings events around the country, of whether to persist with his aggressive strategy towards Truss and her approach to the economy.

One ally of Truss said: “He can either ramp it up again or he can be more considered — but that would an admission of defeat.” Sunak’s team said the ex-chancellor would continue to make his points robustly.

Meanwhile, Labour leader Sir Keir Starmer said the BBC1 debate was illustrative of a party that had “lost the plot” and “lost any sense of purpose”. 

He told the BBC: “I see Rishi Sunak, who was running the economy until just a few weeks ago, acting as if he’s just come down from the moon, realised how bad everything is . . . 

“Then you’ve got Liz Truss who’s voted for 15 tax rises now in this sort of graduate of fantasy economics where she’s making promises without telling us how she’s going to fund them.”

Truss and Sunak are due to face each other again on Tuesday evening in a debate hosted by the broadcaster TalkTV and the Sun newspaper.

In recent days, senior Conservatives have voiced concern at the increasingly negative tone of attacks and briefings by allies of Truss and Sunak.

One former cabinet minister said: “It is just a godsend for the Labour party and damages the perception of the Tories.”