Keir Starmer, the Director of Public Prosecutions, will lead the review, which comes after days of explosive allegations against the late Jim'll Fix It and Top of the Pops presenter who died in October last year.

Dozens of victims have come forward to accuse Savile of abuse since an ITV documentary earlier this month.

In 2009, Surrey Police submitted a file to the Crown Prosecution Service which contained references to four potential offences, including an allegation of indecent assault on a young girl at a children's home. But the case was dropped due to a lack of evidence.

Mr Cameron said prosecutors would also look at whether other relevant authorities, thought to include social workers, should be notified even if prosecutions did not proceed. He said: "The Government will do everything it can do, [and] other institutions must do what they can do, to make sure we learn the lesson of this and it can never happen again."

He also told MPs the BBC had "serious questions" to answer over Savile.

On Tuesday, the BBC's director-general, George Entwistle, admitted there had been problems with the culture at the corporation during the 1970s and 1980s.

He said the BBC was currently investigating nine allegations against current staff and contributors.

Children's charity NSPCC said it had received 161 calls relating to Savile, which have been passed to police.

It has also emerged the BBC and Culture Secretary Maria Miller are engaged in a battle over the independence of the broadcaster.

Ms Miller has said the BBC's handling of the scandal raised "very real concerns".