Jimmy Savile inquiry claims another child abuser 'could be lurking undiscovered at BBC'
The report adds: "Three of Savile's victims were only nine years old."
It is understood that the report will be officially published within six weeks.
Some who work at the BBC told the inquiry in interviews that they had heard about Savile's predatory sexual conduct.
However they feared reporting concerns to managers, it is claimed.
The report reads: "I heard of incidents that took place in virtually every one of the BBC premises at which he worked.
"These included the BBC Television Theatre (in connection with Jim'll Fix It), at Television Centre (in particular in connection with Top of the Pops), at Broadcasting House or Egton House (where he worked in connection with BBC Radio 1), Lime Grove studios and various provincial studios, including Leeds, Manchester and Glasgow.
"He would indulge in sexual touching while working on the set (of Top of the Pops or Jim'll Fix It) and on at least one occasion, he was actually on camera.
"Savile would seize the opportunity for sexual contact even in public places such as corridors, staircases and canteens."
The report is more than 500 pages long, and was finished a year ago but has not yet been seen until it leaked last night.
Commenting on the culture at the BBC in the report, Smith wrote: "Several witnesses described the BBC as very deferential.
"My general impression is that most staff (other than those who had been in the higher echelons) felt that the management culture was too deferential and that some executives were 'above the law'.
"I have the clear impression that most people in the BBC held the talent in some awe and treated them deferentially; they appeared to have the ability to influence careers and were themselves untouchable.
"It would be a brave person indeed who would make a complaint against such a person."