David Cameron has called for the BBC and police to fully investigate claims that Jimmy Savile raped or molested at least 40 women.
And in a further indication of the tarnishing of Savile's reputation, trustees of charities set up by the late TV star are considering dropping his name amid fears that the sexual abuse allegations could taint the organisations indefinitely.
The Jimmy Savile Charitable Trust and Jimmy Savile Stoke Mandeville Hospital Charitable Trust have also announced that they are to donate a portion of their funds to "support charities that work with survivors of sexual abuse".
The barrage of allegations have materialised in the wake of the an ITV documentary that was aired last week.
In the documentary, numerous women claim that they were molested by the TV star with one even claiming that she saw Savile molest girls with convicted paedophile Gary Glitter and one other, as yet unidentified, TV personality.
40 women have come forward with allegations against Savile
Speaking on the Andrew Marr Show, Cameron said: "I think it is pretty shocking, the allegations that we are reading. They need to be properly looked at, properly investigated.
"It seems to me it is very important that the BBC does that itself."
He added: ""But also, if there are questions that should be pursued by the police and other organisations, everyone has to ask themselves the question 'Is there new evidence that needs to be looked at'?"
The call comes as more details of Savile's sordid lifestyle have emerged. The Sunday Telegraph has reportedly heard tapes which appear to show that Savile molested girls whilst broadcasting live on air.
In one tape, Savile can be heard telling a screaming girl: “Watch how I operate… I better play a record with the other hand.”
On another tape a girl can be heard saying: “Get off… Get off my backside.”
The tapes are now in the hands of police and will be used in any investigation.
Describing Savile, Davies said: He was an intriguing subject and something approaching a friendship developed between us.
"Yet despite his generosity and entertaining company, nagging doubts persisted.
"He boasted how many girls would be available to him on a typical night in one of his dancehalls and claimed to have ‘loved them all’."
Davies also spent some time aboard a cruise ship with Savile and recounts, what is in hindsight, a rather chilling and prescient tale: "During our time at sea I was alarmed by how often he stopped elderly couples and used the same quip each time to the husband. ‘You want to be careful about being seen with underage girls,’ he’d say, motioning to the man’s wife. ‘You can get in trouble for that.'"