Kershaw also said that everyone working at the station in the '80s "joked about Jimmy Savile and young girls".
The 54-year-old - who currently presents a show on BBC Radio 6 Music - joined Radio 1 in 1987 and said that the station had thankfully transformed beyond recognition since the 1980s.
She described the past atmosphere at the studios as "intimidating" and told Radio 4's Today programme that she remembered an unnamed presenter fondling her breasts while she was live on the radio.
"I couldn't say anything, I couldn't even explain because I was broadcasting to the nation," she admitted.
"When I complained to somebody, they were incredulous, and said, 'Don't you like it? Are you a lesbian?"'
Kershaw - who began her career at Radio 1 around the time when Savile left the station - said: "The rumours were there, the jokes were there. It was an open secret.
"Round Radio 1 everyone joked about Jimmy Savile and young girls. The main jokes were about his adventures on the Radio 1 Roadshow. It was massive then.
"It was rather like The X Factor going round the country. Can you imagine the X Factor judges rounding up the contestants and asking for sexual favours after the show? I don't think so."
Kershaw - who joined the station from BBC local radio in West Yorkshire added: "When I walked into Radio 1 it was a culture I have never encountered before.
"I have always said it was like walking into a rugby club locker room and it was very intimidating for a young woman."
Upon hearing of Kershaw's claims, a BBC spokesman said: "We are shocked by allegations that anything of this sort could have been carried out by anyone working for the BBC.
"They are allegations which the police have the proper powers to investigate. We would encourage anyone with information on such issues to also speak to the police."
The ITV documentary which recently brought Savile's alleged past actions to light was watched by 1.72 million people on Wednesday (October 3).
Metropolitan Police have since confirmed that they have met officials from the BBC who were "fully co-operating with detectives" following the claims.