Revelations about Savile, who died last year, provoked outrage across Britain where he had been a household name since the 1960s.
News of Savile's crimes threw his main employer the BBC into turmoil, led to resignation of the BBC's director general just 54 days into his job and provoked awkward questions for his predecessor Mark Thompson, who recently took over as chief executive of the New York Times.
Detectives launched their inquiry 10 weeks ago following reports in a TV documentary that Savile had abused young girls on BBC premises and at hospitals where he did charity work.
Since then, 450 people had come forward with allegations about Savile, mostly dealing with sexual abuse, said police.
Savile was now a suspect in 199 crimes, the vast majority of them involving children or young people, the force added.
"These levels of reporting of sexual abuse against a single individual are unprecedented in the UK," the police said in a statement.
Detectives have been examining three categories of alleged offences: those involving only Savile, which make up the majority of cases; those involving Savile and others; and those which had no direct link to Savile.
So far six men have been arrested and another questioned by London police.
Those quizzed include Max Clifford, Britain's most high-profile celebrity publicist, former BBC radio DJ Dave Lee Travis and former glam-rock singer Gary Glitter.
They have all denied any wrongdoing.
"Our officers will continue to investigate allegations made against those who potentially can be brought to justice," the police statement said. "More arrests nationally will be forthcoming."
A one-time professional wrestler with a penchant for garish outfits, Savile became famous as a pioneering DJ in the 1960s before hosting prime-time TV shows until the 1990s.
He ran about 200 marathons for charity, raising tens of millions of pounds for hospitals, leading some to give him keys to rooms where victims now allege they were abused.
