Kennedy first met close friend Mel Giedroyc, who was appearing with the Cambridge Footlights, at the Edinburgh Festival in 1988. Later she became a script editor for Giedroyc's double act with Sue Perkins, and worked as a writer for the Mel and Sue series Late Lunch. Kennedy presented the last series of The Real Holiday Show on Channel 4 in 2000. She has since made appearances in TV comedies Goodness Gracious Me, This Morning With Richard Not Judy, Jonathan Creek alongside Alan Davies and Caroline Quentin, People Like Us and hit BBC comedy The Smoking Room, along with appearing in several of The Mark Steel Lectures, as well as in several plays and radio shows. She was also a movie reviewer on Five's Terry and Gaby Show. In addition to this, she has made several appearances on Big Brother's Little Brother. She provided voices for The Comic Side of 7 Days and was a regular on the BBC Radio 2 comedy That Was Then, This Is Now with Richard Herring. She appeared in the film Notes on a Scandal and also appears in the Five series Suburban Shootout and Suburban Shootout 2: Clackers at Dawn. She appeared as a regular on the popular podcast As It Occurs To Me until June 2011, when the series ended. Active in Comic Relief, Kennedy, with Emma Freud, was involved in setting up the kazoo orchestra concert at the Royal Albert Hall, on 14 March 2011, which broke the Guinness World Record for the largest such ensemble. She also acts the voice of Becky Butters on the CBBC programme Strange Hill High, a series that utilised Japanese vinyl puppets and CGI; that programme was in production during 2013 and 2014. In July 2012, she posed for Tatler in their "Out and Proud - Seven of London's smartest and loveliest lesbians" photoshoot.
Writing career
Kennedy has written for radio, television and the theatre. Her first book, How To Bring Up Your Parents, loosely based on her blog, came out in August 2007. Her second book, The Tent, The Bucket and Me, recounting her childhood camping experiences, was published in April 2009. This was adapted by Kennedy as writer of the six-part BBC TV series The Kennedys, starring Katherine Parkinson, Dan Skinner, Harry Peacock and Emma Pierson, first broadcast on 2 October 2015. The comedy centres on a family living in Stevenage New Town in the 1970s, "when suburbia discovered sophistication". Kennedy has also written children's books. Three books in the Wilma Tenderfoot series have appeared: Wilma Tenderfoot and the Case of the Frozen Hearts, Wilma Tenderfoot and the Case of the Putrid Poison and Wilma Tenderfoot and the Case of the Fatal Phantom. I Left My Tent In San Francisco, the follow-up to The Tent, The Bucket and Me, appeared in May 2011. She has also written a guide to TV series The Killing.
Cookery
Kennedy took part in Celebrity MasterChef in 2012, winning the final after a week of cookery-based tasks, in which ex-footballer Danny Mills and TV presenter Michael Underwood also participated.