The prime minister has said it is “very important… that the rules are followed” after becoming embroiled in a row about a donor paying for his wife’s clothes.

The Conservatives are calling for an investigation into Sir Keir Starmer over a possible breach of parliamentary rules after he failed to declare his biggest personal donor, Lord Alli, paid for a personal shopper, clothes and alterations for Lady Victoria Starmer.

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A Number 10 spokesperson told Sky News it was an oversight that had been corrected after it “sought advice from the authorities on coming to office”.

But it raised further questions over whether Sir Keir and his wife needed to have clothes donated to them when the prime minister’s annual salary is around £160,000.

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This year alone, Sir Keir has received – and disclosed – nearly £19,000 worth of work clothes and several pairs of glasses from Lord Alli, the former chairman of online fashion retailer Asos, The Times reported.

In addition, the peer, whose personal wealth is estimated at £200m, spent £20,000 on accommodation for the now prime minister during the election and a similar sum on “private office” costs, which was also disclosed, the paper said.

MPs are required to register gifts and donations within 28 days of receiving them, but it is understood the donations for Lady Victoria’s clothes were submitted late.

Asked about the row while on a trip to Rome, the prime minister said: “It’s very important to me that the rules are followed. I’ve always said that. I said that before the election. I reinforced it after the election.

“And that’s why shortly after the election, my team reached out for advice on what declarations should be made so it’s in accordance with the rules.

“They then sought out for further advice more recently, as a result of which they’ve made the relevant declarations.”

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Sir Keir added: “For me, it’s really important that the rules are followed.

“That’s why I was very pleased my team reached out proactively, not once, but twice, because it is very important that we have transparency, very important that you and others can see the rules are being followed.”

In a letter to the parliamentary standards commissioner, the Tories highlighted how Lord Alli had hit the headlines over the summer for being given a security pass to Number 10, despite having no government role.

“It has now emerged that at the same time Sir Keir Starmer failed to declare a substantial gift of designer clothes, tailoring and a personal shopper bought for his wife by Lord Alli, both prior to the general election… and following it,” they wrote.

Shadow science and technology secretary Andrew Griffith added: “It beggars belief that the prime minister thinks it’s acceptable that pensioners on £13,000 a year can afford to heat their home when he earns 12 times that but apparently can’t afford to clothe himself or his wife.

“While his top team want a taxpayer-funded clothes budget to look sharp, people across the country are forced to make tough choices in the face of Labour’s damaging decisions.

“Labour promised change but in ten short weeks all they’ve delivered is a change of clothes for themselves. Labour have made the political choice to put themselves and their Union paymasters before the most vulnerable.”