A second woman, who also did not wish to reveal her identity, met Sir Jimmy Savile in 1968 when she was 15. She claimed the star had sex with her for the first time in a London hotel.
She told the ITV1 documentary: "It was a complete shock to me. I had no idea what was happening. I was very young and naive. I just feel that he took huge advantage of me."
Jimmy Savile was questioned as a suspect by police investigating the Yorkshire Ripper, according to a retired police officer.
Jimmy Savile's nephew has spoken of the emotional turmoil his family is going through in the wake of the sex abuse allegations.
A colleague of Jimmy Savile allegedly raped a woman on BBC premises in 1970, ITV News has been told.