Just 7% of voters have confidence that Rishi Sunak will tackle sleaze in British politics.
The shock findings follow the sacking of Nadhim Zahawi as Tory chairman after he was found guilty of multiple breaches of the ministerial code over a probe into his tax affairs.
Sunak is also coming under mounting pressure to sack his deputy, Dominic Raab, over bullying claims made against him by dozens of civil servants.
The poll by People Polling for GB News, also shows little public appetite for Boris Johnson to return to government.
And it confirms that the Conservatives continue to trail more than 20 points behind Labour.
Those taking part in the poll were asked how confident they were that Sunak - who marks 100 days as PM today - could eradicate sleaze from British politics.
Only 1% said they were “completely confident”, with a further 6% saying they were “confident”.
By contrast, 55% said they were “not confident at all”.
Sunak’s ratings were barely any better among Conservative voters, with just 3% of them “completely confident” in his ability to tackle sleaze. Meanwhile, 82% of Labour voters said they were “not confident at all”.
At prime minister’s questions yesterday, Keir Starmer said: “The Tory Party’s addiction to sleaze and scandal has done huge damage to this country and the cost to the public keeps adding up.”
Politics expert Professor Matt Goodwin said: “Amid the fallout from Nadhim Zahawi’s resignation and ongoing stories about sleaze and bad behaviour around the Conservative Party, we find that very few voters are confident Rishi Sunak can clean up politics and remove sleaze.
“On the contrary, more than half the electorate say they are ‘not confident at all’ he will be able to take care of sleaze.”
Amid calls for Boris Johnson to replace Zahawi as Tory chairman, the poll found that 56% of voters either “strongly opposed” or “opposed” his return to cabinet, with only 21% supporting it.
Even among Tory voters, just 47% said they support him returning, with 30% opposing it.
Overall, the poll puts Labour on 46%, with the Conservatives on 22% and the Lib Dems on 9%.
Professor Goodwin said: “The Conservative Party’s share of the national vote remains as flat as a pancake, at a historic low level of support.
“There is little evidence Rishi Sunak, whose own ratings were also down last week, is turning the boat around. The party is still headed for a heavy wipeout at the general election unless things change and, before then, a bruising set of local elections in the spring.”