The claim -- made by the former Radio 1 disc jockey Liz Kershaw -- follows a string of damning allegations of rape and sexual assault levelled against Sir Jimmy Savile.
Kershaw said in a BBC interview yesterday: "There was one presenter who routinely groped me. I would be sitting in the studio with my headphones on, my back to the studio door, live on air. . . and then I'd find these wandering hands up my jumper fondling my breasts.
George Entwistle, the BBC's new director general, who has launched an inquiry into the allegations against Savile, will now meet with Kershaw, who was prevented from naming her alleged attacker on air for legal reasons.
The police inquiry into sexual offences that Savile and others around him may have committed is likely to widen to include audio tapes of Savile apparently abusing young girls. The tapes, in which a teenage girl shouts at Savile to "get off my backside" and another in which a girl screams and Savile says: "I better play a record with the other hand"Dexter series
date back to the mid-1970s but have now been passed to detectives investigating the allegations.
He may now also be implicated in the suicide in 1971 of a 15-year-old girl who appeared as a dancer on Top of the Pops.
According to Clair McAlpine's diary she claimed to have been "used" by presenters and other celebrities at the time. Her cousin Ray Calcutt, 52, told The Sunday Telegraph: "It wasn't properly investigated at the time. There are a lot of nervous people out there from that era."
In the radio interview, Kershaw did not pull any punches when talking about Savile. "The rumours were there, the jokes were there. It was an open secret, and with all the piety about him when he died last year, I was rather sickened and I thought: 'Why don't people say what he was really like?'
"Around Radio 1, everyone joked about Jimmy Savile and young girls. The main jokes were about his adventures on the Radio 1 Roadshow, where they went around the country.
"It was rather like TheSouth Park Season 14
X Factor going round the country then. Can you imagine X Factor judges rounding up the contestants and asking for sexual favours after the show? I don't think so."