Lord Patten, who heads the BBC Trust, has pledged to get to get to the truth following the Jimmy Savile scandal, stating "our public expects no less".
Writing in the Mail on Sunday, Lord Patten says: "even those of us who weren't there are the inheritors of shame".
He adds: "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? Were reports of criminality put aside or buried?"
Amid the fallout from the Jimmy Savile scandal the BBC is investigating nine allegations of sexual harassment among staff and contributors.
BBC boss George Entwistle has spent almost two hours taking questions from MPs about the corporation's handling of the Savile scandal.
Ex-BBC boss Mark Thompson has told ITV News he will help with any inquiry into the corporation and its handling of the Savile allegations.