Boris Johnson has claimed there was “no interest to declare” amid growing pressure over his links to a US businesswoman while he was mayor of London.

After allegations that Jennifer Arcuri received favourable treatment because of their friendship, the prime minister said on Sunday that everything was done with “full propriety”.

Arcuri joined trade missions led by Johnson when he was mayor and her technology company received thousand of pounds in sponsorship grants.

On Friday, the prime minister was referred to the police complaints body to assess whether he should face a criminal investigation over his links.

The Sunday Times reported this weekend that Arcuri confided to four friends that they had been engaged in an affair during his time in City Hall.

In an appearance on BBC One’s The Andrew Marr Show, Johnson insisted “everything was done with full propriety”.

Pressed on whether he declared an interest relating to his links with Arcuri, he said: “There was no interest to declare.”

Marr did not ask about the Sunday newspaper allegations that Johnson had a physical relationship with Arcuri.

The Sunday Times said that David Enrich, now the finance editor of the New York Times, had said he had been told of the alleged relationship in 2013 by two of Arcuri’s friends when he was working for another newspaper. He said: “Two friends from her business class said they had been told by Ms Arcuri that she was sleeping with Boris. They told me that before and after that story ran.”

His account was said to have corroborated that of other sources who had spoken to Arcuri.

The Independent Office for Police Conduct (IOPC) is now considering whether there are grounds to investigate the prime minister for the criminal offence of misconduct in public office.

The Greater London Authority, the city’s devolved government, wrote to Johnson on Friday noting claims that he had on more than one occasion used his position as mayor to benefit and reward Arcuri and saying it had referred the matter to the police watchdog. Johnson was referred to the IOPC because while he was mayor, he was the head of the Mayor’s Office for Policing and Crime, a role equivalent to being police and crime commissioner for the capital.

The statement from the GLA was denounced by Downing Street as a “nakedly political put-up job” on the eve of the Conservative party conference.

The Guardian disclosed on Friday that Arcuri, whose company is being investigated over its eligibility for a £100,000 taxpayer-funded grant, won a highly sought-after entrepreneur visa to stay in the UK after securing the prime minister’s endorsement for her firm.

Months after Johnson helped to raise the profile of her firm, Innotech, by giving keynote speeches at two of its first events, Arcuri won a place on a prestigious government-run visa scheme, giving her firm £15,000 in public funds.

The Guardian also understands that Arcuri attended an event hosted at Buckingham Palace by the Duke of York in December 2014. Her latest company, Hacker House, apparently later claimed to have the backing of Prince Andrew for a scheme providing cyber badges for children.