Boris Johnson has broken his silence on allegations that he misused public funds in grants made to a close female friend, insisting he did nothing wrong.

Asked about his relationship with Jennifer Arcuri, an ex-model and US technology entrepreneur, a US technology entrepreneur, the prime minister said: “I can tell you absolutely that everything was done entirely in the proper way.”

Labour has demanded an investigation by Whitehall’s most senior civil servant, after Ms Arcuri was also handed a privileged place on Mr Johnson’s overseas trade trips when he was London mayor.

On a plane to New York, Mr Johnson had refused – six times – to answer any questions, including whether he had a “sexual relationship” with the American businesswoman.

But, speaking to the BBC, he insisted: “All I can say is I’m very proud of what we did when I was mayor of London, very proud of everything that we did, particularly banging the drum for our city and country around the world.”

He then insisted there had been no wrongdoing – but still declined to discuss the allegations in any detail.

The evidence that Ms Arcuri received £126,000 in public money – including £10,000 from a City Hall organisation, while the prime minister was mayor – threaten to derail his trip to the United Nations.

The Sunday Times reported that Mr Johnson was a regular visitor to Ms Arcuri’s flat in Shoreditch, east London, and attended numerous events promoting her fledgling company.

Ms Arcuri was also given preferential treatment when it came to joining overseas trade missions led by Mr Johnson on three occasions, the report said.

Her business was alleged to have failed, initially, to meet the eligibility criteria for any of the three trade trips she attended in the space of just a year.

As mayor, Mr Johnson was bound by the Greater London Authority‘s code of conduct “to declare any private interests relating to their public duties and to take steps to resolve any conflicts arising in a way that protects the public interest”.

He was also expressly barred from providing any undue benefits to friends.

Labour’s shadow Cabinet Office minister Jon Trickett said the allegations should be probed by cabinet secretary Sir Mark Sedwill.

“With Boris Johnson refusing to answer questions about these allegations of serious conflicts of interest, abuse of power and misuse of public funds, the cabinet secretary should launch an investigation,” said Mr Trickett.

“Despite what his life of privilege has led him to believe, Johnson is not above the law and cannot duck and dodge responsibility. This is a matter of the integrity of the prime minister, who appears to think he can get away with anything.”

The Department for Digital, Culture, Media and Sport is investigating the claim that a business operated by Ms Arcuri obtained a £100,000 grant for UK-based companies to train people to avoid cyberattacks, despite being based in the US.