Scotland Yard detectives said there could be 20 to 25 victims in total and Savile's pattern of offending behaviour was on "a national scale".
He had a "predilection for teenage girls," Commander of specialist crime investigations Peter Spindler told reporters.
Spindler said that police had recorded eight allegations against the long-time BBC presenter, including two rapes.
He added the alleged victims were mainly girls who were aged between 13 and 16 at the time.
He also said that the allegations spanned four decades - with the earliest dating back to 1959.
Spindler's statement came after British Prime Minister David Cameron today called for the BBC and the police to investigate fully claims of sexual abuse against Savile.
Savile, known for his cigars and jangling jewellery, died in October last year aged 84.
"Information is coming in as we speak probably," Spindler told reporters.
"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," he was quoted as saying by the BBC.
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 see if they will co-operate, he said.
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."
A documentary aired last week contained accounts from women who claimed they were sexually assaulted by Savile when they were children, some of them on BBC premises.
George Entwistle, the BBC's new director general, has said the British Broadcasting Corporation would examine all "outstanding questions" once police inquiries into a growing number of allegations were completed.
Meanwhile, Savile's family have been outraged by the claims, arguing that he is unable to defend himself.
