Angela Rayner cannot be fully transparent about the tax arrangements on her second home because there is a court order barring her from revealing the relevant information, Downing Street has said.

The deputy prime minister has been under scrutiny for days over her purchase of a flat in Hove on the south coast and whether she deliberately arranged her financial situation to avoid paying tax.

So far Rayner has not commented personally on the controversy, though colleagues have said she says she has done nothing wrong.

Downing Street revealed on Monday that one reason for her silence was that there was a court order in place that made it difficult for her to speak on the matter. “There is a court order which restricts her from providing further information, which she’s urgently working on rectifying in the interests of public transparency,” No 10 said.

Last week the Conservative party chair, Kevin Hollinrake, wrote to Laurie Magnus, the prime minister’s adviser on ministerial interests, asking him to investigate whether or not Rayner had broken ministerial rules.

Officials say Magnus has not begun an investigation, suggesting he does not believe there is enough evidence to warrant further inquiry.

Keir Starmer gave Rayner his full backing on Monday. She has come in for criticism since she bought the flat in Hove for £800,000 shortly after she removed her name from the deed of her constituency home in Greater Manchester.

Because the flat was then classified as her primary home, she avoided having to pay £40,000 more in stamp duty than she would have done if it had been her second property. Meanwhile, she has listed the constituency house as her primary residence for the purposes of council tax, meaning she does not have to pay council tax on her grace-and-favour apartment in Admiralty House in Whitehall.

Over the weekend it emerged that she had put her Greater Manchester home partly into a trust in 2023, an arrangement that could help her children avoid paying inheritance tax should they take ownership of it after she dies. The property was listed at the time as having a value of £650,000 – the threshold for paying inheritance tax on a bequest from two people.

The Conservatives have been keen to use the complicated financing arrangements to attack the deputy prime minister. Last week Hollinrake in his letter to Magnus accused Rayner of “hypocritical tax avoidance, by a minister who supports higher taxes on family homes, high-value homes and second homes”.

He asked the standards adviser to look specifically at whether she should have paid more stamp duty when she bought the flat in Hove.

Starmer praised his deputy on Monday, saying her critics were making a mistake by attacking her. “Angela has had people briefing against her and talking her down over and over again,” he told BBC Radio 5 Live. “It’s a big mistake, by the way. Angela is an incredible person [and] deputy prime minister.”

Referring to Rayner’s impoverished upbringing, Starmer added: “I think we should be proud as a country that Angela Rayner is our deputy prime minister. That will give I don’t know how many working-class children – particularly girls – a real sense of aspiration. They will look at Angela and think, and I can do something like that. What a brilliant thing.”

It follows a similarly supportive statement from the education secretary, Bridget Phillipson, who said on Sunday: “If an individual wants to buy a property, whether that individual is Angela Rayner or anybody else, they are entirely within their rights to spend their money as they choose. Angela Rayner, as an adult with a salary, is able to make choices about how she spends her own money.”