The Tory party chairman has faced mounting questions over his personal payments to HMRC, but the prime minister has so far stood by him.
Some senior Tories believe it is now impossible for Mr Zahawi to continue in his job, with one describing the situation as “unsustainable”.
The revelation that Mr Zahawi was forced to pay the penalty – part of a reported total tax settlement of almost £5m – comes as The Independent reveals how he tried to gag this newspaper from revealing that he was being investigated by the National Crime Agency and HMRC last year.
In an extraordinary exchange last July, Mr Zahawi repeatedly threatened to sue if any stories were published, saying:
• One hundred per cent I will take legal action
• There was no such investigation by the NCA. I have paid all due taxes and obeyed all financial laws and regulations.
• I repeat I will take legal action
Mr Zahawi also paid a 30 per cent penalty to HMRC, according to a report in The Guardian, taking the estimated total to more than £4.8m – though his spokesperson told the newspaper he “does not recognise this amount”.
Labour last night called on the prime minister to sack Mr Zahawi.
Angela Rayner, the party’s deputy leader, said: “Rishi Sunak promised a government of integrity, professionalism, and accountability but instead he's propping up a motley crew of scandal-ridden ministers.”
She added: “The position of the man who was until recently in charge of the UK's tax system and who this prime minister appointed Conservative Party chair is now untenable.
“It’s time for Rishi Sunak to put his money where his mouth is and dismiss Nadhim Zahawi from his cabinet.”
One Conservative former minister said told The Independent Mr Zahawi’s position was “unsustainable”, because the former chancellor would be asked about his tax affairs every time he appeared in public.
The party would be left with a “chairman that can’t do media [interviews]”, he said, a role that is especially crucial around the upcoming local elections, which are already predicted to be difficult for the Conservatives.
Another former minister said there was a risk the row would “hang over” Mr Zahawi and “overshadow” the role of party chairman.
“A judgement needs to be made about whether this storm can be weathered and a line is drawn or it hangs over the chairman and overshadows [his role as party chairman],” they said.
“It is a conversation behind closed doors that needs to be had – about if he can fulfil his duties,” they added.
Mr Zahawi was seen by many MPs to have done a good job in the short time he has been in the role.
At the weekend The Sun on Sunday reported that he had settled a tax dispute relating to an offshore company registered in Gibraltar to hold shares in the polling company that he co-founded, YouGov.
YouGov's 2009 annual report showed a more than 10 per cent shareholding by the Gibraltar-registered Balshore Investments Ltd, and described the company as the “family trust of Nadhim Zahawi”. At the time Mr Zahawi was an executive director of YouGov.
A spokesperson for Mr Zahawi has previously said that his taxes are “properly declared and paid in the UK” and the minister “has never had to instruct any lawyers to deal with HMRC on his behalf”.
During the week, Mr Sunak defended his party chairman, telling MPs at Prime Minister's Questions that Mr Zahawi “has already addressed this matter in full and there’s nothing more that I can add”.
The prime minister's press secretary also said Mr Zahawi “has spoken and been transparent with HMRC”.
On whether Mr Sunak believed the matter was now closed, she said: “I don’t know whether the prime minister has reviewed it in full, but I do know that he takes Nadhim Zahawi at his word.”
Mr Zahawi’s spokesperson did not respond to requests for comment.
A HMRC spokesperson said: “We are unable to comment on identifiable taxpayers due to strict confidentiality rules.”
No 10 declined to comment.
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