The family of Sir Jimmy Savile are removing the headstone from his grave out of "respect to public opinion" after police said the former presenter could have abused up to 25 victims over 40 years.

Savile's family said they wanted to ensure the "dignity and sanctity" of the cemetery in Scarborough.

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. A plaque outside his home has been defaced.

On Tuesday, police said that Savile's abuse might have been on a "national scale".

Scotland Yard has formally recorded eight criminal allegations against the former Top Of The Pops presenter 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.

Commander Peter Spindler, head of specialist crime investigations at Scotland Yard, said the allegations span four decades, the earliest of which dates back to 1959. Mr Spindler said although it is early in the inquiry, the information so far suggests Savile possessed a "predilection for teenage girls".

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. The pattern of his offending behaviour does appear to be on a national scale."

Mr Spindler said the first allegation dates back to about 1959 but most claims seemed to be from the 1970s and 80s.

Scotland Yard has contacted ITV and the BBC, which in turn are contacting alleged victims to see if they will co-operate, he said. Mr Spindler added: "We believe there are probably another 20 potential victims there. 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."