Rishi Sunak and his wife have recognised her tax “situation” was “not favourable”, says a government minister – as the chancellor launched an inquiry into the leaking of details about her non-dom status.

After the disclosure that Akshata Murty was “non-domiciled” in Britain for tax purposes sparked a political storm, policing minister Kit Malthouse told Sky News that her decision to now pay UK taxes on all her worldwide income meant the issue had been “corrected”.

Days of revelations about Mr Sunak’s household arrangements – including his multi-millionaire wife’s finances and his past US residency status – have raised questions over his political future.

The chancellor has bristled at the questions over Ms Murty, describing them as “smears” and a source close to Mr Sunak now says an “aggressive” leak inquiry will look at the possibility of criminal prosecution for whoever is responsible.

Opponents have homed in on estimates that the chancellor’s wife’s tax arrangements may have saved her tens of millions of pounds – with the revelations coming even as national insurance rises last week added to the squeeze on working households.

Sources close to Mr Sunak have played down reports that he has moved his wife and two daughters out of the chancellor’s residence in Downing Street to escape the glare of the media – saying that his family were just spending more time at their west London home as their eldest daughter is in her last year at primary school.

Mr Malthouse, who previously served as deputy to Boris Johnson when he was mayor of London, appeared to acknowledge some of the criticism, during an interview with Sky’s Trevor Phillips.

He said Ms Murty’s announcement that she had decided to pay UK taxes on all her income showed she had accepted that there was a “sense of disquiet” about the situation and she had “moved to correct it”.

“She is a non-combatant in the political fray but I think both she and Rishi have recognised that that situation was not one that was favourable and it was distracting from the overall message.

“He’s put a huge amount of effort, time, commitment and energy into helping this country get through the last couple of years and it’s unfortunate that his wife has been drawn into this political fray in this way.

“They’ve now corrected that situation – hopefully we can move on.”

Mr Malthouse was also pressed on the revelation that the chancellor – who previously lived in the US – still held a permanent residency green card for the country even after he had returned to the UK, entered British politics, and moved into Number 11.

Mr Sunak made a statement disclosing his possession of a green card – and how he has now handed it back – last week, confirming initial reporting by Sky News.

The minister said his understanding was that the status was a “hangover from that time” that Mr Sunak had lived in America and that very often the green card “just lapses and gets removed”.

He denied the suggestion that the chancellor’s career was now “toast” and said he had been a “remarkable force for good in this country over the last two years”, adding “I’m a big fan.”

Mr Malthouse told the BBC, on the non-dom status revelations, that “obviously it’s not a brilliant time for it to come out” and “seemed to be anomalous to lots of people” while offending “a British sense of fair play”.

He added, on the scrutiny facing the chancellor: “It is not ideal but we all, when we sign up to this job, know that there’s going to be rough times and smooth times.”

On the chancellor’s future political prospects, he said: “What happens to him in future will be of secondary importance to what happens to the country.”

Labour’s deputy leader Angela Rayner, meanwhile, mocked the decision to hold a leak inquiry over the revelations, tweeting “Keep my wife’s taxes out of your mouth” in response – an echo of actor Will Smith’s words during his now infamous recent Oscars ceremony appearance.

Ms Rayner also taunted the chancellor about the suggestion – which has been denied – that briefing against the chancellor came from Number 10.

“The leaking of any member of the public’s tax affairs is of course very serious, but he might just want to ask next door?,” she said.