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Police investigating the alleged sexual abuse of girls by the late Sir Jimmy Savile are pursuing 120 separate lines of inquiry, Scotland Yard has said.

Police said they had recorded eight allegations against him, including two rapes, and there could be 30 victims.

Separately, his headstone will be removed from his grave in Scarborough after his family expressed concerns.

Meanwhile, Freddie Starr has denied claims he groped a 14-year-old girl in a ´óÏó´«Ã½ dressing room with Savile.

In an interview with the ´óÏó´«Ã½, he said of the allegations made by Karin Ward in an ITV documentary: "They're not true. I'm totally innocent."

The comedian said he would welcome the opportunity to speak to police about the claims.

Earlier, police said the probe into the Jimmy Savile abuse allegations would be a joint inquiry with children's charity the NSPCC and would be named Operation Yewtree.

During a press briefing at the Metropolitan Police headquarters in London, police said the alleged victims were mainly girls who were aged between 13 and 16 at the time, and the allegations spanned four decades.

"At this stage it is quite clear from what women are telling us that Savile was a predatory sex offender," said Commander Peter Spindler, head of specialist crime investigations, in an interview with the ´óÏó´«Ã½.

"It's vital that those who have been victims of that actually get the recognition and acknowledgement and support that they deserve."

Cdr Spindler said that of the eight criminal allegations, six were alleged indecent assaults on teenage girls.

He said Savile's pattern of offending behaviour appeared to be on "a national scale" and he had a "predilection for teenage girls".

Cdr Spindler said the first allegation dated back to about 1959 but most seemed to be in the 70s and 80s.

The briefing was told that a range of different names had been reported to police, as well as Savile's.

Cdr Spindler said police were not investigating the ´óÏó´«Ã½. But he said Scotland Yard had been in contact with ITV and the ´óÏó´«Ã½ to gather information. He said they were also contacting alleged victims the organisations have been talking to to see if they would co-operate.

Asked if allegations related to any institutions other than those mentioned in previous claims - the ´óÏó´«Ã½, Jersey children's home Haut de la Garenne, or Duncroft Approved School in Staines, Surrey - he said he had contacted Stoke Mandeville Hospital and Leeds Royal Infirmary.

Cdr Spindler said police wanted a swift conclusion to what he described as an "assessment" rather than an investigation.

He said it was being carried out by Scotland Yard and being led by its serious case team, which looks at complex and historical cases. Seven staff are working on it, and this would be increased to 10 on Wednesday, he added.

Cdr Spindler said a provisional search of Scotland Yard's records could not find any record of any previous investigation into Savile, and they were only aware of the previous involvement of Surrey Police.

The aim of the investigation is to produce a final joint report with the NSPCC, looking at the lessons learned and sharing the findings with other relevant agencies, he said. Police hope to produce the report by the end of next month.

Peter Liver, of the NSPCC, said the charity had had 17 calls to its helpline directly related to the allegations.

´óÏó´«Ã½ home editor Mark Easton said the inquiry had the capacity to expand quite considerably.

He said there was something specific about the 1960s and 1970s, in which sexual liberation collided with traditional male-dominated power structures, and powerful men took advantage of the situation.

Meanwhile, it emerged that Savile's headstone, which was erected in Scarborough on 20 September and bears the epitaph "it was good while it lasted", is to be removed on Wednesday.

A bottle was thrown at it last week but it was not damaged, North Yorkshire Police said.

"The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery," Savile's family said in a statement.

"Out of respect to public opinion, to those who are buried there, and to those who tend their graves and visit there, we have decided to remove it."

On Monday, ´óÏó´«Ã½ Trust chairman Lord Patten said the corporation must "command credibility" in how it dealt with the allegations.

Earlier on Monday, ´óÏó´«Ã½ director general George Entwistle promised a "comprehensive examination" of allegations that Savile abused girls while working for the corporation.

Savile died in October 2011, at the age of 84.

The face of Top of the Pops in the 1960s, he hosted TV favourite Jim'll Fix It on ´óÏó´«Ã½ One in the 1970s and 1980s and was knighted in 1990 for his charity work.

But recently allegations have spread about serious sexual assaults on under-age girls at the height of his fame.

Some of the allegations - publicised in an ITV documentary - refer to incidents on ´óÏó´«Ã½ premises.