So far 12 allegations of sexual offences have been officially recorded but this number is increasing, the force said yesterday.
Metropolitan Police detectives are in contact with 14 other forces as the number of allegations against the late television presenter continues to rise.
Since ITV screened a documentary in which five women alleged they had been abused, new claims about Savile’s predatory behaviour have emerged on a daily basis. They include allegations that he targeted young hospital patients at Leeds General Infirmary.
A man has also claimed that he was abused by Savile as a 10-year-old boy in the notorious Jersey care home Haut de La Garenne.
The developing scandal has seen the BBC come under fire with allegations that the corporation was aware of the Jim’ll Fix It presenter’s behaviour and failed to take action.
David Nicolson, who worked as a director on the children’s programme, claimed to have caught Savile having sex with a girl in his dressing room, but said he was laughed away when he voiced his concerns.
He said: “It was a bog standard changing room in the basement. They both quickly pulled up their pants. The girl could have been 16, maybe 15. But she was just one of many – he always had one in the room.”
When he reported the incident, he said he was told: “That’s Jimmy. I was revolted by his behaviour. They just shrugged it off, saying ‘Yeah, yeah – that’s the way it goes’.”
Mr Nicolson added: “Everyone knew what was going on. That includes senior BBC people – chiefs at the highest levels.”
It was also claimed yesterday that Savile was banned from visiting a council-run children’s home after he molested a 12-year-old girl.
A woman, who did not want to be identified, said he was told to leave the care home in Leeds after staff found him in a bedroom with the girl in the 1970s.
She said the girl was indecently touched by the former DJ but that a social worker advised her not to report it to the police.
The witness said that the woman in charge of the home, who seemed “uncomfortable” with Savile visiting, “ran upstairs and found him” when she realised he had taken the girl into a bedroom.
She said: “You could hear it –there were raised voices from the staffroom and then she just ran upstairs.
“A social worker came down and basically he came back the next day and said it would be his word against Jimmy Savile and it would be unfair to put a girl through the procedure of a police investigation that probably will end in nothing and ruin a man’s career.”
Leeds Safeguarding Children Board said it had not received any complaints about Savile but encouraged anyone with concerns to report them.
Deputy Prime Minister Nick Clegg said he thought the Savile case was “the dark side” of Britain’s celebrity culture.
The Sheffield Hallam MP said: “I have been thinking about this a lot because I just cannot understand how this remained hidden for so long. There must have been just so many people who knew what was going on in hospitals, the BBC, maybe in the police.
“I just keep asking myself why did this remain buried for so long. The only explanation I can come up with is what we are seeing is the dark side of the culture of celebrity, and actually in this case it wasn’t a culture of celebrity, it was the cult of celebrity.
“I get the impression people felt that with all that glitter and shine there can’t be a dark side, there can’t be a seedy side. We need to teach our kids, because there is such a celebrity culture at the moment, that however rich you are, however famous you are, however glamorous you are, everyone has to live by the same rules.”