Claire was bought up in her birth place Hemel Hempstead by her parents who are a shopkeeper and an Irish-born secretary. She was educated at Cavendish School in Hemel Hempstead, but her dream of being an actress meant her attention was overted from her school work and she "barely scraped through [her] A-levels." She then went on to study at the London Academy of Music and Dramatic Art and then later on joined the Royal Shakespeare Company.
She landed her first role in 'Hanky Park', by Walter Greenwood at the Oldham Repertory Theatre. Since then she has gone on to appear in numerous television roles, perhaps best known for her role as Clare in the British TV comedy 'Life Begins'. Most recently she has starred as Sue in the BBC's comedy 'Outnumbered'.
She is currently married to director Charles Palmer, the son of actor Geoffrey Palmer.