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Surrey police has confirmed that Sir Jimmy Savile was questioned over allegations of child sex abuse in 2007.
In a statement, they said an individual was interviewed over offences which were "alleged to have occurred at a children's home" in the 1970s.
The matter was referred to the Crown Prosecution Service, which "advised there was insufficient evidence to take any further action".
A documentary detailing similar allegations is due to air this week.
The broadcaster, who died last year, is accused of sexual abuse against under-age teenage girls in the ITV1 investigation, to be shown on Wednesday.
Several alleged victims speak on the programme. They say the abuse took place in hospitals, schools and BBC buildings.
In a statement, the BBC said it had found no evidence of abuse taking place on its premises.
"Whilst the BBC condemns any behaviour of the type alleged in the strongest terms, in the absence of evidence of any kind found at the BBC that corroborates the allegations that have been made it is simply not possible for the corporation to take any further action."
The broadcaster's nephew, Roger Foster, added that his family was "disgusted and disappointed" by the programme.
But fellow broadcaster Paul Gambaccini said he had been "waiting 30 years" for such stories to come out.
Speaking on ITV1's Daybreak programme, he said newspapers had been primed to run similar stories while Sir Jimmy was alive, but the star had intervened to prevent their publication.
"On [one] occasion, and this cuts to the chase of the whole matter, he was called and he said 'well you could run that story, but if you do there goes the funds that come in to Stoke Mandeville - do you want to be responsible for the drying up of the charity donations'. And they backed down."
No charges were ever brought against the broadcaster when he was alive.