Rishi Sunak’s political distancing from Nadhim Zahawi has taken another step, with Downing Street refusing to say the prime minister is confident the Conservative party chair has been consistently honest about his tax affairs. Sunak’s decision to order an inquiry by his new ethics adviser notably failed to limit the fallout from Zahawi’s still-opaque dealings with HMRC, while a former Tory minister called for him to step aside while the investigation took place. No 10 has not given a vigorous defence of Zahawi after it emerged he resolved a multimillion-pound tax dispute by paying a penalty, but seems content to let him stay on as party chair and a cabinet minister, to the disquiet of some Conservative MPs. Asked on Tuesday if Sunak believed Zahawi had always told him the truth about tax, the prime minister’s spokesperson said there had not been discussions between the pair “on that specific level of detail”. Asked if Sunak thought Zahawi had been honest more generally, the spokesperson said: “I don’t have much to add beyond what the prime minister set out yesterday. There is some ongoing work now by the independent adviser to ascertain the facts. And I think it’s right that he’s allowed to carry out that work, rather than me cutting across it.” The policing minister Chris Philp, who was sent out to speak for the government on Tuesday morning, similarly opted to duck questions about Zahawi’s actions and said people should wait for the findings of the inquiry. Asked how Zahawi had been “careless” – the Tory chair’s description – in reporting his affairs to HMRC, Philp told the BBC: “I don’t know what form that carelessness took and nor, probably, does anybody else apart from HMRC and Mr Zahawi, so let’s find out the facts.” It is now established that Zahawi paid a penalty to HMRC to settle a tax dispute while he was Boris Johnson’s chancellor, a position giving him ultimate oversight of the tax system. However, it remains unclear what Sunak knew and when. No 10 sources have briefed that when ministers are vetted before appointment, HMRC officials only say whether someone has a tax matter outstanding and nothing else, meaning Sunak would not have been warned because Zahawi had paid the balance by then. However, a source in the government said No 10 had been aware of the details when Zahawi was made Tory chair and the minister without portfolio in October. The former immigration minister Caroline Nokes welcomed the inquiry by Sunak’s ethics adviser, Sir Laurie Magnus, saying there were “too many unanswered questions”, but argued Zahawi should step aside while it took place. “When you become the story, it’s a distraction from anything else the government’s trying to do,” she told TalkTV. “There are countless examples of good, competent cabinet colleagues who got themselves in a mess, who have resigned and in some instances returned just a few months later. And I think in order to get this cleared up, Nadhim should stand aside and let the investigation run its course.” With no indication of how long Magnus will take – officials have said only that he hopes to make the process as fast as possible – some Tory backbenchers have vented their frustration. “It doesn’t look good if we’re trying to move away from the scandals of the Boris era,” one MP said. “You would have thought that the lesson from the past nine months is that if someone is mired in scandal, don’t let them hang around.” One apparent hurdle for Zahawi if he is to remain in the cabinet is not just what happened with his tax, but how he explained it before acknowledging the HMRC settlement at the weekend. In July, a spokesperson for Zahawi, then the chancellor, said all his taxes were “fully paid and up to date” and that he was not aware of an HMRC investigation. A day later, Zahawi told Sky News he had “always declared my taxes”. A key consideration for Magnus will be whether Zahawi has abided by the Nolan principles of public life, which underpin the ministerial code. One of these sets out that people in public life “should be truthful”. This principle also holds true for statements to the media, with the precedent of Damian Green, who was sacked as Theresa May’s de facto deputy prime minister in 2017 after admitting he lied about pornographic images on his House of Commons computer. Asked if Zahawi would be dismissed if he had been found to have been dishonest, Sunak’s spokesperson said: “I’m simply not going to pre-empt the work of the independent adviser. The prime minister thinks it is right to allow him to establish the facts and present his findings.”