Labour leader Sir Keir Starmer is likely to seize on the fallout from Mr Zahawi’s multi-million pound settlement at Prime Minister’s Questions on Wednesday.
The Prime Minister ordered his ethics adviser to investigate whether Mr Zahawi broke ministerial rules over the estimated £4.8 million bill he settled with HMRC while chancellor.
Mr Sunak admitted there are “questions that need answering” as the inquiry was launched but it was unclear what he knew when appointing Mr Zahawi to the Cabinet-attending role.
Chairman of the Committee on Standards in Public Life Lord Evans criticised the legal threats Mr Zahawi made as he tried to prevent stories about his tax affairs emerging.
As they worked to uncover the situation, The Independent website said he personally threatened “legal action” and tax lawyer Dan Neidle was contacted by “expensive” libel lawyers.
Lord Evans suggested “trying to close down a legitimate public debate” would not live up to the Nolan principles on public life that must be upheld under the ministerial code.
“Accountability, openness are things which the Government says that it wants to be characterising its own behaviour, so that I think speaks for itself,” he told BBC Radio 4’s PM programme.
“The sort of attempts, apparent legal attempts to suppress this story, I don’t think that does live up to the sort of standards that the public would rightly expect.”
Senior Conservative MP Caroline Nokes has called on him to “stand aside until this matter is all cleared up” but Mr Sunak has so far stood by Mr Zahawi.
The Prime Minister argued it is “longstanding practice” for ministers to remain in their roles while under investigation.
Just last Wednesday, Mr Sunak told PMQs that Mr Zahawi had “already addressed this matter in full”.
The Prime Minister’s press secretary said Mr Sunak “takes Nadhim Zahawi at his word”.
But Mr Sunak bowed to pressure to order the investigation by ministerial interests adviser Sir Laurie Magnus after the Guardian revealed Mr Zahawi paid a penalty as part of the dispute.
Downing Street subsequently suggested Mr Sunak did not know last week that Mr Zahawi had paid the reportedly 30% penalty to HMRC.
And the Prime Minister said that the advice he received ahead of appointing Mr Zahawi party chair in October was that there was “no reason” not to.
Mr Zahawi, the MP for Stratford-upon-Avon, has insisted his “error” over shares in the YouGov polling company he co-founded was “careless and not deliberate”.
He has insisted he is “confident” he has “acted properly throughout”.
Labour has argued Mr Sunak should sack the chairman before the investigation’s conclusion, describing it as a “pathetic attempt to pass the buck”.
Mr Zahawi was appointed chancellor by Boris Johnson, whose time in No 10 was continuing to create challenges for Mr Sunak.
Fresh allegations of cronyism in the Tory party have been levelled after it emerged BBC chairman Richard Sharp helped secure Mr Johnson a loan of up to £800,000 before the then-PM backed his appointment to the broadcaster.
Since the last PMQs, Mr Sunak has also received a second police fine, this time for failing to wear a seatbelt after he broke coronavirus rules during the partygate scandal.