Jimmy Savile may have abused as many as 25 victims over a 40-year period on a "national scale", police have said.
Scotland Yard has formally recorded eight criminal allegations against Savile so far in its investigation, named Operation Yewtree.
The alleged abuse involves teenage girls as young as 13 and includes two complaints of rape and six of indecent assault, with officers looking into up to 120 lines of inquiry.
The scale of the alleged abuse by the former Top of the Pops presenter was disclosed as Savile's family planned to remove the headstone from his grave to ensure the "dignity and sanctity" of the cemetery.
A family spokesman said in a statement: "The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery.
"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."
A number of memorials to Savile have already been removed, including an inscription on the wall at Leeds Civic Hall in recognition of his charity work, and a street sign in Scarborough, North Yorkshire.
Commander Peter Spindler, head of Specialist Crime Investigations, said the abuse was on a "national scale" and that the allegations spanned four decades.
Mr Spindler said they believed there may be as many as 20 other victims.
He told reporters: "Information is coming in as we speak probably.
"The reality is this really has captured the public's mind. We are getting calls from victims, from witnesses and third parties who believe they know something about it.
"We have formally recorded eight criminal allegations against Savile. Two of those are rape, six of indecent assault.
"These are primarily against girls in their mid-teens, so between 13 and 16 and it spans four decades of abuse."
Although it is in its early stages, he said allegations suggested Savile's "predilection for teenage girls".
"There is a pattern of behaviour that is being presented to us which ultimately we will hope to analyse and present in a final report in some weeks time," he said.
Mr Spindler said they are working to identify anyone who could be subject to criminal investigation. The BBC is not being investigated, he said.
He said the first dated back to about 1959 but most seemed to be in the 70s and 80s.
The NSPCC said it had received 40 calls over the last five days following claims of sexual abuse committed by Jimmy Savile.
"Of these, 24 have been referred to the police or other agencies," a spokesperson for the charity said.
"Seventeen of the calls directly related to Jimmy Savile," they added.
"Just as importantly 21 people spoke to our counsellors about abuse they had suffered from other people – not Savile- and were given advice and referred to other support agencies where appropriate," the NSPCC said, urging victims of abuse to contact their helpline.
Scotland Yard has been in contact with ITV and the BBC to gather information and they are contacting alleged victims they have been talking to to see if they will co-operate.
Mr Spindler added:
"It is too early for us to give you an accurate picture of what 120 lines of inquiry will distil down to but we believe we will come up with between 20 to 25 victims."
Mr Spindler said victims would be looking for an "acknowledgement and a recognition of what happened to them."
"You really shouldn't underestimate the impact even after so many years of reliving these experiences and then to watch the public debate unfold and it has been quite significant," he said.
"It will be traumatic for some, if not all, of them."
Mr Liver from the NSPCC added: "I just want to acknowledge the bravery of the victims of abuse that have come forward as a result of this inquiry."
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Updated 18:35 9 October 2012: headstone information