Keir Starmer, the Director of Public Prosecutions, said yesterday he had asked his top legal adviser to re-examine four files submitted by Surrey Police three years ago, including claims that the late television presenter indecently assaulted young girls at a children's home.
David Cameron said the Government would do everything it could to ensure that such abuse could never happen again and said Mr Starmer would consider moves to help victims in cases where no prosecution was brought.
The Crown Prosecution Service (CPS) decided in 2009 that there was not enough evidence to bring charges against Savile on the grounds that the alleged victims did not want to give evidence in court.
The chief Crown prosecutor for the South East, Roger Coe-Salazar, reviewed the files after an ITV documentary earlier this month unleashed a torrent of allegations against Savile.
He concluded that the correct decisions were taken at the time based on the information and evidence then available.
However, Mr Starmer has decided "out of an abundance of caution" to give the papers in the four cases to his principal legal adviser, Alison Levitt QC, so she can look at them and advise him.
The Director of Public Prosecutions said: "Whilst it is sometimes possible to prosecute cases where the victim does not support a prosecution, there are obvious problems in proceeding with a case where the victim does not support a police investigation, where there is no forensic evidence and only very limited, or even in some instances no, witness evidence, particularly in relation to allegations which date back a number of years.
"This is not a straightforward issue but I have said to the Attorney General that I would like to discuss with him whether the CPS should adopt a policy of referring cases to other relevant agencies, such as social services, where an allegation is made but cannot be proceeded with for evidential reasons."
Speaking at Prime Minister's Questions yesterday, Mr Cameron said: "The Director of Public Prosecutions specifically is going to consider what more can be done to alert relevant authorities where there are concerns that a prosecution is not taken forward.
"The Government will do everything it can do, other institutions must do what they can do, to make sure that we learn the lesson of this and it can never happen again."
Scotland Yard said it had identified more than 200 potential victims of Savile and other people, including some who were still alive.
The NSPCC children's charity said yesterday that it had received 161 calls relating to the television presenter, details of which had been passed to police.
A lawyer representing more than 20 alleged victims of Savile said some of them claimed to have been abused by a "paedophile ring" at the BBC.
Liz Dux, of solicitors Russell, Jones and Walker, said in an interview: "It was very organised. It was not just Savile, there were other people behind it."
George Entwistle, the BBC's director-general, told MPs on Tuesday that between eight and 10 former and current BBC staff and contributors had been named as alleged perpetrators of sexual abuse.
A BBC spokesman said: "The BBC has stated that anyone with information or allegations of this kind should speak to the police."