Yesterday, new BBC director general George Entwistle was told by MPs to "get a grip" on his organisation during a tempestuous session at the Commons culture, media and sport select committee.
Entwistle had said Savile's alleged behaviour could have been enabled by a "broader cultural problem" at the BBC, and conceded that the corporation had been too slow to react to the crisis.
But he also revealed that the BBC is investigating up to 10 of its current and former staff and contributors following serious allegations of "sexual harassment, assault or inappropriate conduct" in the fallout of the Savile scandal.
The BBC has ordered two investigations into the 'Savile affair' - one will look at the culture and practices of the BBC when the Jim'll Fix It host worked there, and the other will investigate the decision to drop a Newsnight report on the allegations of sexual abuse against Savile last December.
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In a letter to BBC Trust chairman Lord Patten, culture secretary Maria Miller warned that the scandal raised "very real concerns" over public trust in the BBC.
She said that it was important that the two investigations were "able to follow the evidence wherever it takes them".
However, Lord Patten was firm in his response to the letter, insisting that the investigations will be "comprehensive and independent",
"You know how seriously the Trust takes the allegations surrounding Jimmy Savile and the need to maintain public trust in the BBC," he wrote.
Tellingly, the peer added: "I know that you will not want to give any impression that you are questioning the independence of the BBC."
However, Sir Roger Gale told the Evening Standard that this response shows the BBC chairman is "out of touch", and suggested that both Entwistle and Patten may have to "fall on their swords" following the scandal.
"Chris Patten is an old friend and a former parliamentary colleague for whom I have had a high regard but in his comment he has made it clear that he is out of touch, not only with the strength of feeling and concern in Parliament about the 'Savile affair' and related matters but, more importantly, with the strength of public revulsion at what has happened at Television Centre and with the corporate culture that, for the best part of 40 years, has apparently covered it up," he said.
"Attack may be the best form of defence but in seeking to criticise a culture secretary who has not, ever, sought to challenge the independence of the BBC, he indicates how very little, within that corporate arrogance, has really changed."
Sir Roger added: "The 'Auntie knows best' line simply does not wash any more. BBC management, over far too many years, has sought to maintain an imperious disdain for criticism and it has become clear that successive directors general have, while happy to criticise others for not answering difficult questions, either turned a blind eye to criminal activities or have not known what has been going on on their own doorstep, which is also culpable.
"It is as if your favourite and respectable aunt has been revealed to be on the game and if Lord Patten is not able to grasp that, then I fear that not only the director general but also the chairman of the BBC Trust are going to have to fall on their swords."
But former BBC chairman Sir Christopher Bland said that it would be unwise to "jump to conclusions" before the two BBC inquiries are completed.
"What it needs to do is await the result of the two inquiries because at the moment the noise of people jumping to conclusions is almost overwhelming and the truth is we don't know the truth," he said.
"It needs to be absolutely forensic and ruthless in its search for the truth. If you followed up every rumour or allegation about the BBC as chairman or director general, you would have no time for your proper job."