Deputy Prime Minister Nick Clegg said he thought the Savile case was "the dark side" of Britain's celebrity culture.
"I just cannot understand how this remained hidden for so long," he told BBC Radio Five Live.
"There must have been just so many people who knew what was going on in hospitals, the BBC, maybe in the police.
"I just keep asking myself why did this remain buried for so long. The only explanation I can come up with is what we are seeing is the dark side of the culture of celebrity, and actually in this case it wasn't a culture of celebrity it was the cult of celebrity."
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.