Louise Mensch, who is also a novelist, yesterday published an email exchange with a man claiming to be an investigative journalist who made allegations about her time in the music industry during the 1990s.
Among them were claims she took drugs at Ronnie Scott’s in Birmingham and danced with Mr Kennedy while drunk in front of a group of journalists.
The MP for Corby and East Northamptonshire said: “Although I do not remember the specific incident, this sounds highly probable.
She added: “I thoroughly enjoyed working with Nigel Kennedy, whom I remember with affection.
“Additionally, since I was in my 20s, I’m sure it was not the only incident of the kind; we all do idiotic things when young.
“I am not a very good dancer and must apologise to any and all journalists who were forced to watch me dance that night at Ronnie Scott’s.”
Mr Kennedy said: “I am a socialist myself but do remember having some great times with my beautiful and very clever right wing friend. Louise is pretty scary and I would warn anyone that it’s not a good idea to mess with her.”
Mrs Mensch rapidly built up a high media profile after being elected last May, particularly for her role as a member of the Culture, Media and Sport Committee that grilled the Murdochs and Rebekah Brooks over phone hacking.
The mother of three has penned a series of successful chick-lit novels, selling more than two million books worldwide, and recently married Peter Mensch, manager of rock group Metallica, dropping her previous surname Bagshawe.
Allegations in the email also include a claim she was sacked from her job as an EMI Press officer because she wrote novels of a “sexual nature” during work hours.
Mrs Mensch admitted to writing some of her first book, Career Girls, on her work computer but only after hours.