Cdr Spindler said a provisional search of Scotland Yard's records could not find any record of any previous investigation into Savile, and they were only aware of the previous involvement of Surrey Police.
The aim of the investigation is to produce a final joint report with the NSPCC, looking at the lessons learned and sharing the findings with other relevant agencies, he said. Police hope to produce the report by the end of next month.
Peter Liver, of the NSPCC, said the charity had had 17 calls to its helpline directly related to the allegations.
BBC home editor Mark Easton said the inquiry had the capacity to expand quite considerably.
He said there was something specific about the 1960s and 1970s, in which sexual liberation collided with traditional male-dominated power structures, and powerful men took advantage of the situation.
'Comprehensive examination'
Meanwhile, it emerged that Savile's headstone, which was erected in Scarborough on 20 September and bears the epitaph "it was good while it lasted", is to be removed on Wednesday.
A bottle was thrown at it last week but it was not damaged, North Yorkshire Police said.
"The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery," Savile's family said in a statement.
"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."
On Monday, BBC Trust chairman Lord Patten said the corporation must "command credibility" in how it dealt with the allegations.
Earlier on Monday, BBC director general George Entwistle promised a "comprehensive examination" of allegations that Savile abused girls while working for the corporation.
Savile died in October 2011, at the age of 84.
The face of Top of the Pops in the 1960s, he hosted TV favourite Jim'll Fix It on BBC One in the 1970s and 1980s and was knighted in 1990 for his charity work.
But recently allegations have spread about serious sexual assaults on under-age girls at the height of his fame.
Some of the allegations - publicised in an ITV documentary - refer to incidents on BBC premises.
http://www.bbc.co.uk/news/uk-19887019