A senior Tory peer and former Commons standards chair appeared to suggest that Nadhim Zahawi should step away from his Conservative Party role while the inquiry into his tax affairs continues.

Lord Young of Cookham, who served in a range of Conservative administrations from Margaret Thatcher to Theresa May, suggested that under-pressure ministers should feel able to step aside for the duration of any investigation.

It will only add to calls for the Tory chairman to stand down while under investigation for settling a multimillion-pound tax dispute while chancellor.

Mr Zahawi has authorised HMRC to discuss his settlement – estimated to be worth £4.8 million and includes a penalty – with the ethics investigation ordered by Prime Minister Rishi Sunak.

In a difficult week for Downing Street, pressure on ministers grew after HMRC boss, Jim Harra, told MPs there are “no penalties for innocent errors in your tax affairs”.

Speaking to BBC Radio 4’s Week in Westminster programme, Lord Young said: “Last year, a minister was accused of an impropriety. He resigned and he was cleared.”

In an apparent reference to former minister Conor Burns, who had the Tory whip restored after being cleared of misconduct at the party conference in October, he said: “I think what a prime minister should do in those sorts of circumstances is bring the minister back and I think that would give out a signal that is not the end of your career if you stand back while the inquiry takes place.

“You can be rehabilitated if, indeed, allegations are proved to be untrue,” said the peer, who chaired the Standards and Privileges Committee for nearly a decade.

The senior Tory said that a prime minister had to be “fair” to any minister facing damaging allegations.

But he said that he hoped the inquiry into Mr Zahawi would not “take too long”.

“I think that’s a real problem that some of these inquiries. One recent parliamentary one took three years before it was resolved. So, I think, it’s quite difficult to short-circuit the system. Without having all the facts, there’s a real risk of injustice.”

He also called for the report into Mr Zahawi to be published “in full”, as well as adding his voice to calls for the Government’s ethics adviser to be able to initiate their own investigations.

“I think a signal would be if that report was published in full. We’ve been promised a summary. Well, I’d quite like to see the whole report.”

It comes as HMRC admitted that it had made mistakes in the handling of a freedom of information (FOI) request centred on the tax affairs of ministers.

The Financial Times reported that in response to an inquiry by the paper last year, HMRC said that no minister was being investigated.

But at the time, Mr Zahawi was the subject of a probe by tax officials.

The paper reported that a response to a freedom of information request by tax lawyer Dan Neidle, who had been working to expose Mr Zahawi’s tax affairs, was believed by HMRC staff to be incorrect after he was informed that it was a backbench Tory MP and not a minister who was under investigation.

“We acknowledge that the processing of this FOI request was subject to a series of administrative errors, which we very much regret.

“We corrected these errors as soon as they came to light and are confident that our most recent response to Mr Neidle was both accurate and in line with the Information Commissioner’s Office guidance,” a HMRC spokesperson said.

A Liberal Democrats source said that the party is planning a “Shakespearean tragedy” in Mr Zahawi’s Stratford-on-Avon seat, with the constituency added to leader Sir Ed Davey’s tour of England ahead of the local elections in May.

Both the Lib Dems and Labour have called on Mr Zahawi to stand aside, but those calls have been so far resisted by both the prime minister and the Tory chairman.

Amid the furore over his tax arrangements, Mr Zahawi visited a barbershop in his constituency on Friday, posting photos of the engagement on Twitter on Saturday morning.

Speaking during a Cabinet away day at Chequers on Thursday, Mr Sunak told broadcasters: “I’m not going to pre-judge the outcome of the investigation, it’s important that the independent adviser is able to do his work.

“That’s what he’s currently doing, that’s what I’ve asked him to do and I’ll await the findings of that investigation.”

A week ago, Mr Sunak told Prime Minister’s Questions that Mr Zahawi had addressed the fiasco “in full”.

But he went on to launch an investigation by Sir Laurie Magnus, his independent adviser on ministers’ interests, admitting there were “questions that need answering” after the penalty was revealed.

Mr Sunak insisted that “no issues were raised with me” when he appointed Mr Zahawi to his current role, amid questions over his political judgment.