Angela Rayner has said she understands why some voters are perturbed by donations accepted by her and other government ministers, while arguing that a complete stop to such gifts would require a wider debate about how politics is funded.

The UK deputy prime minister pushed back strongly against claims she might have not properly declared donations such as accommodation on a holiday in New York, saying she had done everything necessary.

She made the comments as Labour gathers for its first annual conference since winning the election, a celebratory event that has nonetheless been dogged by criticism over donations to senior government figures, including clothes for Rayner and the prime minister, Keir Starmer.

On Friday, it was announced that ministers would no longer accept gifts of clothes following the controversy about donations by the Labour peer Waheed Alli funding Starmer’s work wardrobe, as well as clothes for his wife, Victoria, that were not initially declared.

It has emerged that Rayner and Rachel Reeves, the chancellor, had also accepted clothing.

Rayner told BBC One’s Sunday with Laura Kuenssberg show: “I get that people are frustrated, in particular the circumstances that we’re in, but donations for gifts and hospitality and monetary donations have been a feature of our politics for a very long time.

“People can look it up and see what people have had donations for, and the transparency is really important. I get that people are angry, I get that people are upset.

“I think the transparency is there so people can see that. Now, if there is a national debate about how we fund politics and how we do that, and I hear that people are frustrated with that, but we have a system at the moment that says if you get donations, that has to be declared and the rules have to apply to everybody.

“I think that is correct so people can see where you’ve had donations and where that potential influence is so that people can see the transparency.”

She denied any wrongdoing over a stay in a New York apartment owned by Alli while she was on holiday there. She said: “I don’t believe I broke any rules. I had the use of the apartment and I disclosed that I had the use of the apartment.

“In fact, I think I was overly transparent because I think it was important despite it being a personal holiday because that person, as a friend, had already donated to me in the past for my deputy leadership.”

Speaking earlier to Sky News, Bridget Phillipson, the education secretary, said she had accepted donations for a 40th birthday event and another reception because they were held “in a work context”.

She said: “The reason that we can have this conversation is because colleagues have followed the rules. I followed the rules. I’ve set out in the register of interests what donations were for, who they were from, and that’s there for the public to see.”

The row continues to dominate coverage in many newspapers, with the Mail on Sunday featuring a front-page photograph of Starmer and David Lammy, the foreign secretary, with Starmer’s chief of staff, Sue Gray, at Tottenham’s stadium last weekend for the team’s match against Arsenal.

Starmer is a longstanding Arsenal fan and has said he accepts the use of corporate boxes to avoid the expense of security if he sat in the stands.

In a parallel controversy, there has been some hostile leaking from inside government against Gray, who has been portrayed as politically naive and controlling. Cabinet ministers insist privately that this is not true, and that the Downing Street operation is working well.

Asked about this, Rayner said: “I don’t accept that Sue Gray is part of a problem at all and I don’t accept the caricature of how No 10 is working.”

She added: “I’m in No 10. I go in at 8.30 every single morning and I do not see that, and I do not see this caricature that somehow we’re all fighting over mansions or all at loggerheads with each other.

However, there are signs the rows could be affecting the government’s popularity. A poll in the Times by YouGov found that 53% of voters think Starmer is doing badly as prime minister, compared with 34% who say he is doing well.