In 2004, Punch played the receptionist Elaine Denham in Doc Martin. She has worked at the Royal Court and Bush theatres, both in London. She made her stage debut as Elaine in Terry Johnson's West End adaptation of The Graduate. In 2000, Punch appeared in the film Greenfingers.
She starred as a football player in the children's TV show Renford Rejects, and played the role of the victim Melissa Townsend in the 19th episode of Midsomer Murders. Her other TV credits include the naive daughter of Alison Steadman's character in the short-lived series Let Them Eat Cake which starred French and Saunders. Punch made her acting debut in a 1998 episode of The New Adventures of Robin Hood. Punch (left) with the cast of You Will Meet a Tall Dark Stranger in 2010