Boris Johnson has insisted there was "no interest to declare" amid a storm over his association with an American businesswoman when he was mayor of London.
On Friday, the Prime Minister was referred to the police complaints body to assess whether he should face a criminal investigation over his links with former model Jennifer Arcuri.
The Sunday Times has now reported that she confided to four friends that they had been engaged in an affair during his time in City Hall.
It follows reports by the same paper that Arcuri was given £126,000 in public money and privileged access to three foreign trade missions led by Johnson while he was mayor.
But appearing 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 Ms Arcuri, he said: "There was no interest to declare...
"Let's be absolutely clear, I am very, very proud of everything that we did and certainly everything that I did as mayor of London."
And he accused his successor Sadiq Khan of "peddling" the reports, adding: "I may say that the current mayor of London could possibly spend more time investing in police officers than he is investing in press officers and peddling this kind of stuff."
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 by two of Arcuri's friends when he was working for another newspaper.
His account was said by the Sunday Times to corroborate that of other sources who had spoken to Arcuri.
Downing Street refused to comment on the report.
The claims come after the Greater London Authority (GLA) said its monitoring officer had recorded a "conduct matter" against Johnson over allegations Arcuri received favourable treatment because of her friendship with him while he was mayor of London.
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 GLA statement, denounced by Downing Street as a "nakedly political put-up job" on the eve of the Tory Party conference, came after details of Arcuri's links to Johnson were first highlighted in the Sunday Times last week.
Johnson has consistently denied any wrongdoing in relation to his links with Arcuri.
Enrich told The Sunday Times that he had been working on an article on Arcuri's business partner for the Wall Street Journal, published in 2013, when he interviewed her and spoke to a number of people in her close circle.
"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," he told the paper.
The latest allegations of infidelity follow a string of well-publicised stories involving Johnson's private life, some of which plagued his 25 year marriage to second wife Marina Wheeler.
In 2004 he was sacked from the Tory frontbench over a reported affair with journalist and colleague at The Spectator, Petronella Wyatt.
He described claims about the relationship as "an inverted pyramid of piffle" at the time.
Affair claims reared their head again in 2006 when it was reported that the married father-of-four had been romancing Anna Fazackerley of the Times Higher Education Supplement.
The Appeal Court ruled in 2013 that the public had a right to know that he had fathered a daughter during another adulterous liaison with another woman, Helen Macintyre, while mayor of London in 2009.
Despite surviving years of turmoil, Johnson and his lawyer wife separated and began divorce proceedings in 2018 and he is now living at Downing Street with former Tory Party worker Carrie Symonds, 31.
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