The prime minister sought to downplay the row over the flat when he was asked about his gifts from the Labour peer while on a trip to New York, after weeks of questions about receiving clothing, spectacles and temporary use of a £18m penthouse from Alli.

He said there was nothing wrong with having used Alli’s flat for filming during the Covid pandemic, after questions about why he used the peer’s house rather than his own or his office.

“That was just part of a video we were putting out in relation to – I think it was during Covid. Anybody who thinks that I was pretending it was my own home – the idea that I’ve got union jacks by my fireplace at home and or that I would invite a bunch of you lot into my living room to have a look around. I mean, I think the idea that I was trying to pretend that it was my home is pretty farcical. And, no, I’m not going to be inviting you in to film me in front of my fireplace. I’m very sorry, that’s about the last thing I’d do.”

During a meeting with chief executives in New York at the apartment of the UK consul general, Hannah Young, he also appeared to joke about the row, saying: “I’d like to pretend this is my apartment to welcome you too, but I can’t, because Hannah’s already nabbed it.”

Starmer has maintained throughout the row that Alli has never sought to have influence over his government other than helping achieve a Labour victory. The peer, who is a party fundraiser, was given a pass to No 10 in the weeks after the election, but this has now been given up as he has no role in the government.

Starmer has said he borrowed Alli’s £18m penthouse during the election campaign to make sure his son had peace away from protesters and journalists to revise before his GCSEs. He has also said he will not accept more clothes or spectacles from Alli, having taken £16,000 of clothes and more than £2,400 for spectacles during the campaign.

However, the furore over freebies, also including football and concert tickets, appears to have dented Starmer’s popularity in the polls, along with public opposition to the cuts to the winter fuel allowance.

Asked whether he accepted the row had damaged trust in his government, Starmer said: “As I’ve openly acknowledged, I understand why you ask me questions. I understand why the public have questions about this. I think the best thing we can do is to explain the circumstances and be absolutely clear that nothing wrong has been done here.

“Everybody has complied with all of the rules. Sometimes it takes time to go through the individual examples, which may or may not put the context for people to see and make their own judgments. But look, I know why you’re asking questions.”