Kavanagh was educated in Brussels, and trained as a drama teacher at Bretton Hall College and as an actor at Bristol Old Vic Theatre School. Her first known appearance was as Nicky in a 1984 episode of Minder. In 1990 she played the lead in the first production (in Scarborough) of Alan Ayckbourne’s The Revengers’ Comedies, opposite Jon Strickland. In 1985 she appeared in the Doctor Who serial Timelash.

She played Lucy Downes in the Inspector Morse ITV series, in the episode “The Wolvercote Tongue” in 1987. In 1994 she appeared as Penny Winter in eight episodes of Seaforth. The following year she played Rosina Lagrange in three episodes of The Glass Virgin. In 2009 she starred as Christine O’Connell in Doctors (after originally appearing as June Mobley three years earlier). She has also been a member of the BBC Radio Drama Company for BBC Radio 4. In 2016, she played Ms Birling in Stephen Daltry’s production of An Inspector Calls, and played the Doctor’s wife, Patience, in the Doctor Who audio drama Cold Fusion.