A total of 500 alleged victims of Savile, who died last year aged 84, have contacted detectives in the 10 weeks since the investigation was launched.
Officers have recorded 199 crimes in 17 different police force areas around the country in which the former BBC presenter was a suspect, among them 31 allegations of rape in seven force areas.
Some 82pc of those who have come forward to report abuse to police are women, and eight out of 10 of Savile's victims were children at the time.
A Scotland Yard spokesman said: "These levels of reporting of sexual abuse against a single individual are unprecedented in the UK."
The investigation, Operation Yewtree, is examining allegations against other figures from the entertainment world.
The Scotland Yard spokesman said: "Our officers will continue to investigate allegations made against those who potentially can be brought to justice."
The police and the NSPCC children's charity are now compiling a report about Savile's activities, which is due to be published early in the new year.