Parliament’s standards watchdog has opened an investigation into the prime minister over a possible failure to declare an interest when first asked.

The probe by the standards commissioner, Daniel Greenberg, was launched on 13 April and cited paragraph 6 of the MPs code of conduct, which governs how MPs should behave.

The code states that MPs “must always be open and frank in declaring any relevant interest in any proceeding of the House or its committees, and in any communications with ministers, members, public officials or public office holders”.

A Downing Street source said the investigation relates to the shares his wife Akshata Murthy holds in a childcare agency that could benefit from a policy announced in the budget.

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A spokesperson for Number 10 said: “We are happy to assist the Commissioner to clarify how this has been transparently declared as a ministerial interest.”

Mr Sunak faced accusations of a possible conflict of interest after he failed to mention Ms Murthy’s links to Koru Kids when he was questioned by MPs over why the financial announcement favoured private firms.

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The i newspaper revealed that Companies House lists her as a shareholder in the organisation as recently as 6 March.

In a letter to parliament’s liaison committee, which quizzed the PM last month, Mr Sunak said he had declared the interest on the ministers’ register – but rules state that ministers should also update the financial register that exists for MPs.

“I note that there has been some media coverage relating to the minority stake my wife has in relation to the company Koru Kids,” Mr Sunak wrote.

“I was being asked questions by the committee in my capacity as prime minister.

“I would like to clarify for the parliamentary record that this interest has rightly been declared to the Cabinet Office.”

The prime minister said the most recent list of ministerial interests would be published “shortly” by his independent ethics adviser, Sir Laurie Magnus.

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“This regime ensures that steps are taken to avoid or mitigate any potential conflict of interest, and that the interests of ministers’ spouses or partners are not something that would influence their actions either as ministers or as members of parliament,” he added.

Mr Sunak has previously said that “transparency is really important” for parliament to operate well.

In reaction to Sky News’ Westminster Accounts project launched in January, the prime minister said there was a reason that “rules and regulations” are in place.

“I think transparency is really important for the healthy functioning of democracy, it’s absolutely right that there’s disclosures around donations and outside interests,” he said.

Mr Sunak wrote to the liaison committee to follow up on points that were raised at its session with the prime minister last month.

Labour MP Catherine McKinnell pointed out that six private childcare agencies were set to benefit from Jeremy Hunt’s budget, in which the chancellor announced a pilot of incentive payments of £600 for childminders joining the profession – a sum that doubles to £1,200 if they sign up through an agency.

Ms McKinnell quizzed Mr Sunak on the logic behind making the bonus twice as much for childminders who sign up through private agencies.

His response was that the policy was “designed in consultation with the sector”.

Pressed again on the rationale, he said: “I think it’s a reflection of the fact that they are through intermediaries so there are additional costs.

“And, ultimately, we want to make sure the policy is effective in bringing additional people into the system.”

Asked if he had any interest to declare, Mr Sunak replied: “No, all my disclosures are declared in the normal way.”

The Liberal Democrats previously said that Ms Murthy’s shareholding raised “serious questions” for Mr Sunak and called on Sir Laurie to investigate.

And in response to the launch of the investigation, Liberal Democrat chief whip Wendy Chamberlain said: “Another day and another accusation of a Conservative prime minister bending the rules.

“This is on the same day that Rishi Sunak may have broken election rules for his government announcement today.

“After months of Conservative sleaze and scandal, the public just want a government which is focused on the country, rather than saving their own skin.”

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Labour’s Deputy Leader Angela Rayner said: “This government’s failure to update the rules or publish a register of ministers’ interests in nearly a year has left a transparency black hole which is enabling the prime minister and those he has appointed to dodge proper scrutiny of their affairs.

“If Rishi Sunak has got nothing to hide, he should commit to publishing the register before May’s elections so the public can see for themselves.

“While this prime minister fails to deliver the integrity he promised and preserves the rotten standards regime he inherited as the Tories resist tighter rules, Labour has a plan to clean up politics with an Independent ethics and integrity commission to restore standards in public life.”

The prime minister is just the latest MP to investigated by the commissioner, who is looking into the behaviour of six MPs in total.

Last week investigations were opened into three MPs, including former health secretary Matt Hancock, Tory MP Henry Smith and independent MP Scott Benton.