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Former BBC director-general Greg Dyke said he knew nothing of the allegations until two weeks ago.
Speaking on Radio 4's Any Questions, he said: "Jimmy Savile was long gone by the time I got to the BBC, and I hadn't worked there before.
"I look back at who was head of light entertainment in those days, and you come to really quite venerable figures like Bill Cotton and Jim Moir and I cannot believe - these were men of great integrity, I mean Jim Moir was a devout Catholic - I just don't believe they would have condoned this.
"We don't know anybody knew yet and that will be the interesting thing to find out, and that's what the inquiry will find out, who knew. Of course the problem is there's hardly anybody left at the BBC who was there at that time."
In response to reports that the BBC is reconsidering the naming a part of Broadcasting House after the late John Peel, a BBC spokesman said:
"Clearly in the event of proven allegations of sexual abuse, the BBC would reconsider its decision on the naming of part of our new building."
Today's Daily Mail features the claims of a woman, now 59, who says she was made pregnant by John Peel during a three-month affair they had when she was 15.
The BBC has posted the transcript of director-general George Entwistle's statement here.
BBC Director-General George Entwistle said he will not suspend Newsnight editor Peter Rippon.
"I have confidence in Peter Rippon. He's a very good editor indeed," he said.
BBC Director-General George Entwistle told ITV News UK Editor Lucy Manning that he did know that Newsnight was looking into Jimmy Savile, but not that there were allegations of sexual abuse involved.
"I did not know what aspect of Jimmy Savile they were looking into," he said.
"I had no idea of the strength of any information they might have or allegations they were dealing with."
The second BBC inquiry will look at the culture and practice of the BBC "during the years that Jimmy Savile worked here and afterwards," BBC Director General-George Entwistle said.
BBC Director General-George Entwistle said he has ordered an immediate independent inquiry into "whether there were any failings in the BBC management of the Newsnight investigation."
BBC Director General George-Entwistle said the continued speculation about Newsnight's reasons for dropping its investigation into Jimmy Savile is "damaging to the BBC."
BBC Director Genera-George Entwistle has announced two inquiries, both to be led by "independent figures with the ability to command respect for their insight and judgement."
One will examine Newsnight's management and the other will review culture and practice at the BBC during the time Jimmy Savile was an employee.
Latest ITV News reports
Several of Sir Jimmy Savile's alleged victims are considering taking legal action against the DoH and the BBC, a lawyer has told ITV News.
BBC director-general George Entwistle offered a "profound and heartfelt apology" to the alleged victims of Sir Jimmy Savile's sexual abuse.