The American businesswoman at the centre of claims about her links to Boris Johnson reportedly told friends that she had an affair with him while he was mayor of London.

On Friday, Johnson 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.

The paper 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 her 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.

The newspaper reported that Arcuri was given £126,000 in public money and privileged access to three foreign trade missions led by Johnson while he was mayor.