British police have said Jimmy Savile may have abused up to 25 victims some as young as 13 over four decades.
Detectives said they were looking into 120 lines of inquiry about Savile, the late BBC TV star at the centre of a child sex scandal.
The allegations against him were first aired in an ITV documentary just over a week ago.
A number of the alleged victims have gone public, triggering a media storm that has raised awkward questions for the BBC including suggestions the broadcaster covered up Savile's crimes, some of which were said to have taken place on BBC premises.
The BBC's new Director General George Entwistle apologised yesterday to the women alleging abuse by Savile, who died last year aged 84.
Eight women have already made criminal complaints against Savile, two of rape and six of indecent assault.
Commander Peter Spindler, who is heading the police inquiry, said he expected more to follow as other victims came forward.
"We think we will come up with between 20 and 25 victims," he told reporters, adding the eight who had already come forward had mostly been aged 13 to 16 at the time of the alleged abuse.
"The pattern of his offending behaviour does appear to be on a national scale," Spindler said.
He added the abuse spanned four decades with the earliest reported case in 1959.
Cigar-chomping Savile, instantly recognisable by his shock of blonde hair and garish outfits, is accused of using his celebrity status to abuse the girls.
The former DJ travelled around London in a Rolls-Royce and was knighted by Queen Elizabeth for his charitable work in 1990.
When he died last year, he was buried wearing a tracksuit after his gold-coloured coffin was put on public display in a hotel.
Some of the alleged victims have said there was a culture of sexual abuse inside the BBC when Savile was at the height of his fame in the 1970s and 80s, and that other well-known stars were involved.
"We're not investigating the BBC, the only people we will be investigating are specific individuals should there be any evidence," Mr Spindler said, rejecting a suggestion that they were looking at a sex ring inside the broadcaster.
"I'm very satisfied with the level of support the BBC have provided. They are fully cooperating," he added.
As Savile is dead, he himself will not be the focus of any criminal investigation.
Instead, Mr Spindler said their primary objective was to get recognition for the victims and have the issues out in the open.
"Information is coming in as we speak. The reality is this really has captured the public's mind," Spindler said. He said the police inquiry was an assessment rather than a formal investigation at this stage.
Detectives aim to produce a speedy report in conjunction with the National Society for the Prevention of Cruelty to Children (NSPCC) charity to see what conclusions can be drawn.
Last year, an investigation by Newsnight, the BBC's flagship news show, was shelved, prompting critics to suggest that BBC bosses had known about the allegations but kept quiet.
The BBC has denied that. Newsnight's editor Peter Rippon said his decision not to run its story was because the allegations against Savile could not be substantiated.
British Prime Minister David Cameron has called on the BBC to conduct an internal investigation.