The chairman of the BBC Trust, Lord Patten, has expressed his determination to deal with the sexual abuse scandal involving Jimmy Savile.
Writing in the Mail On Sunday, he says the corporation's reputation is on the line and it must face up to the truth.
Lord Patten apologised to those victims who alleged abuse by the TV presenter were not aired by Newsnight.
The Sunday Times says ex-BBC director general Mark Thompson's office was alerted about the Savile abuse claims.
A BBC spokesperson said: "Mark Thompson has repeatedly made clear he had no personal knowledge of the allegations."
Savile's nephew Roger Foster has told BBC Radio 5 Live about how "devastating" the allegations have been for his family.
'Reputation on the line'
It is thought Savile, who died last year aged 84, may have abused scores of young girls and some boys, some on BBC premises, over a 40-year period.
About 300 people may have been victims of sexual abuse, according to Scotland Yard.
Savile is alleged to have carried out abuse at a number of institutions, such as the high security psychiatric hospital Broadmoor, Stoke Mandeville Hospital and Leeds General Infirmary.
The TV presenter and DJ, who was knighted in 1996, was a UK household name in the 1970s and 80s.
In his article for the Mail on Sunday, Lord Patten says the BBC "risks squandering public trust" and its "reputation is on the line" because one of its stars was apparently a sexual criminal.
"Like many who work for the BBC, I feel a sense of particular remorse that abused women spoke to Newsnight, presumably at great personal pain, yet did not have their stories told as they expected," he says.
He also asks whether anybody knew of the abuse allegations.
Lord Patten goes on: "Can it really be the case that no one knew what he was doing? Did some turn a blind eye to criminality?
"Did some prefer not to follow up their suspicions because of this criminal's popularity and place in the schedules?"
The BBC Trust chairman also stresses he has instructed current BBC director general George Entwistle staff must "co-operate fully" with the inquiry, led by former Sky News chief Nick Pollard, into the handling of the Newsnight report.
"The sooner the report emerges the better, but no one should lean on Mr Pollard to cut corners," he warns.
"We want and need a full account of what happened, wherever its conclusions lead. The Trust will publish it and take whatever steps are necessary.
"The BBC must tell the truth and face up to the truth about itself, however terrible."
Elsewhere, the Sunday Times says the former BBC director general's office was formally alerted about the allegations twice - in May and September.
Mr Thompson left the corporation in September to take up a post in the New York Times.
In May, a newspaper journalist contacted the head of Mr Thompson's office about the Savile allegations, but was told to speak to the BBC press office - according to the Sunday Times.
The head of Mr Thompson's office told the paper she did not inform him about the allegations, which are also said to have been laid out in a rejected freedom of information request a few months earlier.
Responding to the article, Mr Thompson's spokesman said he "was not aware of the conversation," adding "he was on holiday at the time and this brief conversation was not relayed to him, either then or subsequently".
The Sunday Times also reports a separate occasion in September, in which an email was sent from ITV - which was investigating Savile - to the BBC editorial policy department and Mr Thompson's office.
A BBC spokesman confirmed the email had been received and sent on to both departments. He added: "We cannot say definitively it did not go anywhere else."
Mr Thompson's spokesman told BBC News: "Mark does not recall being briefed and took no part in the response to the email in early September from ITV relating to its Jimmy Savile documentary. This response was handled by colleagues in BBC Journalism.
"As Mark has made it clear, he had no involvement in the decision not to proceed with the Newsnight investigation into Jimmy Savile."
'A dark side'
Allegations of sexual abuse against Savile have continued to mount since claims were first made public in ITV's documentary at the beginning of October.
On Saturday, Savile's nephew Roger Foster told the BBC he had not believed the allegations at first, but so many had surfaced he was now "convinced that the vast majority of them are true".
He said he could not understand how his uncle, who did so much charity work, "could have such a dark side to him".
The BBC has announced two inquiries as a result of the Savile abuse claims, and a further review into the current sexual harassment policies at the BBC.
On Monday, former Court of Appeal judge Dame Janet Smith will begin a review into the culture and practices of the corporation during Savile's time there, and will also examine whether the BBC's child protection and whistleblowing policies are fit for purpose.
The independent Pollard inquiry is already examining the BBC's management of the Newsnight Savile investigation.