Jimmy Savile may have abused as many as 25 victims over a 40-year period on a "national scale", police say.
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 at Scotland Yard, said the allegations - the earliest of which dates back to 1959 - span four decades, with information suggesting abuse was on a "national scale".
He said: "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."