Boris Johnson has refused to answer questions about his relationship with a young businesswoman who was handed a privileged place on his overseas trade trips when London mayor.

The allegations about the access – plus £126,000 in public money – granted to model-turned-tech-entrepreneur Jennifer Arcuri threaten to dog the prime minister on his trip to the United Nations.

Mr Johnson was a regular visitor to Ms Arcuri's flat in Shoreditch, East London, according to a report in The Sunday Times, and attended numerous events promoting her fledgling company.

But, when asked six times about the explosive allegations by reporters on his plane to New York, the prime minister gave the same reply: “I’m here to talk about what we are doing at the UN.”

The prime minister refused to say whether he denied any conflict of interest, dodged the issue of whether an inquiry was needed to clear up the matter and declined to say if he and Ms Arcuri had been lovers.

Labour has demanded an investigation into the possible misuse of public funds and called on Mr Johnson to resign if he is found guilty of wrongdoing.

Shadow cabinet minister Jon Trickett said: "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.

"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."

According to The Sunday Times, Ms Arcuri, who was in her late twenties at the time of the controversy, described Mr Johnson as “one of her best friends”.

It said evidence showed that, in 2013, her new business received £10,000 in sponsorship cash from an organisation that the future prime minister was responsible for as London mayor.

She was given a £15,000 government grant in 2014, under a programme to encourage foreign entrepreneurs to build businesses in Britain - Ms Arcuri is an American citizen - and, in 2018, a further £100,000 award.

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

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

Initial decisions to turn her down for two of those trips were overturned after intervention by Mr Johnson and his close team in the mayor's office, it was claimed.

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One internal email was said to show how she was given access to a New York trade mission after she discussed the matter with the then-mayor and he was said to have been happy for her to take part.

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 barred from providing any undue benefits to friends.