At Conservative leadership hustings events over the summer Liz Truss supporters have waved placards and sported T-shirts emblazoned with “In Liz we Truss”.

But the faith of Tory party members in the likely next prime minister is far from being reflected across the UK more broadly.

When, as expected, Truss enters No 10 next week to find an in-tray spilling over with difficult issues, the lack of trust in her office will be among the knottiest to resolve.

In recent decades politicians, not least because of Tory sleaze in the 1990s and the MPs’ expenses scandal in 2009, have enjoyed less than the full confidence of the public.

Trust in British democracy and the state has plummeted to new depths under Boris Johnson with his rejection of the normal conventions of government.

When he won a landslide victory in 2019 his relaxed relationship with the truth was already well known – but enough voters were willing to set that aside in return for his boosterism and Brexit promises, and because they didn’t like the alternative of Jeremy Corbyn.

But whatever faith he gained among that part of the population over Brexit, he had already squandered with the rest by proroguing parliament, and later through his willingness to break international law over the Northern Ireland protocol.

Johnson’s constant attacks on Brussels, the judiciary and the civil service may have been convenient politically but they further eroded trust in national institutions.

His hubristic handling of a series of self-inflicted scandals over the last year – Owen Paterson, Partygate and Chris Pincher – left his integrity fatally wounded and public trust even more diminished.

His final days in office have been spent scrabbling in the political gutter, instructing the lawyer Lord Pannick to try to get him off the hook in the forthcoming Commons inquiry into whether he lied to MPs over Partygate.

Just 18% of voters believe Johnson tells the truth “most of the time”, according to pollster Ipsos. But Truss, who has cast herself as the “continuity Boris” candidate in an attempt to shore up the Conservatives’ fragile, but election-winning, voter coalition, does not fare much better on 22%.

She has already said she would vote to scrap the Partygate investigation and has refused to commit to reappointing an ethics adviser, saying she “always acted with integrity”.

“I don’t make promises I can’t keep and I am a straightforward person who tells it like it is,” she said at one party event.

But her record during the leadership campaign, and before that in government, suggests she is not as honest as she likes to claim, and raises questions about whether she will fulfil campaign pledges.

One senior Tory says: “With everything that is stacked against her, Liz needs to be straight with people and to deliver on her promises. All the signs so far suggest that she won’t do either.”

Truss’s claims about her old school in Leeds “letting down” children have been furiously denied by fellow ex-pupils.

She quickly U-turned on her regional pay board plans after northern Tory MPs kicked up a fuss about them undermining levelling up.

She criticised those who “talked the country down” even though she herself suggested British workers lacked the graft of foreign rivals.

The political consequences for her of further undermining trust, transparency and the integrity of government could be huge. The number one trait voters are looking for in a new prime minister is honesty, even ahead of being in touch with ordinary people or a strong leader.

In contrast, her leadership rival Rishi Sunak made “restoring trust” one of the key planks of his campaign, and repeatedly said that would only be achieved by being honest with the public about the economic pain ahead.

Truss has taken a different approach. “I know there are difficult forecasts out there, but forecasts are not destiny,” she told one hustings. “What we shouldn’t be doing is talking ourselves into a recession. We should be keeping taxes low.”

Team Sunak concedes she had the better strategy to win over the T-shirt-wearing, banner-waving Tory membership, but one insider predicts: “That approach will not win the country. She’s promised what she can’t deliver. The worst thing you can do as a party, when people are already disillusioned with politics, is give them even more reasons for that.”