A businessman said to have advised David Cameron has been arrested on suspicion of raping a girl under the age of consent.
Doug Richard was questioned by police and released on bail.
A spokesman for City of London Police said: "City of London Police detectives arrested a 56-year-old man on January 5 2015 on suspicion of inciting a child to engage in sexual activity, sexual activity with a child, meeting a child following sexual grooming and rape of a girl under the age of consent. He was bailed on January 6 until March 2015."
The Sunday Mirror reported that Mr Richard, who starred on BBC's Dragons' Den in the first two series, has travelled with Mr Cameron on an official government trip to Africa and advised on policy.
The American-born married millionaire has also worked as an adviser to Chancellor George Osborne, the newspaper said.
The alleged victim is 13 years old, it added.
The newspaper quoted a statement issued by Mr Richard which said: "I absolutely deny the allegations made about me.
"It would be inappropriate to comment further given that the police are at a very early stage of their investigation."
Mr Richard's association with Mr Cameron goes back to at least 2007, when the then Opposition leader invited the technology entrepreneur to write a report about small business in Britain, the newspaper said.
In 2008, the Californian founded a business loans initiative called School for Startups, alongside the Department for Business, Innovation and Skills, it added, and he remained an adviser after Mr Cameron entered Downing Street in 2010.