Prime Minister David Cameron has called for allegations of sexual abuse made against the late TV presenter Jimmy Savile to be investigated fully.

Speaking on the Andrew Marr Show on Sunday morning Mr Cameron called the claims, which have emerged in recent weeks from a number of women, “truly shocking”.

And he said that the allegations should be investigated further by both the BBC and, if need be, the police.

“I think it is pretty shocking, the allegations that we are reading,” Mr Cameron said.

“They need to be properly looked at, properly investigated. It seems to me it is very important that the organisation, the BBC, does that itself.”

“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’?” he added.

He admitted, “From what I have read – and that is just as a consumer of the media – truly shocking things have been said.”

The reports have come in the wake of an ITV documentary screened earlier this week.

In Exposed: The Other Side of Jimmy Savile, a total of five women claimed they were indecently assaulted by the TV and radio personality when they were schoolgirls in the late 1960s and 1970s.

Historic accounts, which detailed how the presenter allegedly targeted girls in his BBC dressing room and private Rolls-Royce, were shown after Surrey Police confirmed it had referred a historic rape allegation against the Jim’ll Fix It star to Scotland Yard.

Surrey Police also confirmed it investigated Sir Jimmy over abuse claims in 2007, but dropped the case due to a lack of evidence, while Jersey and Sussex Police said they had both received complaints about the star.