She was educated privately at Godolphin School and then Latymer Upper School.
Her feature film credits include Hot Fuzz, Bad Teacher, You Will Meet a Tall Dark Stranger, Dinner for Schmucks and Into the Woods. She performed with the National Youth from 1993 to 1997 and began a course at University College London before dropping out to become an actress. Since 2006 Punch has lived in West Hollywood, Los Los Angeles
Punch made her acting debut in a 1998 episode of The New Adventures of Robin Hood.
Her other television credits include the naive daughter of Alison Steadman"s character in the short-lived series Let Them Eat Cake which starred French and Saunders. She starred as a football player in the kids television show Renford Rejects, and played the role of victim Melissa Townsend in the 19th episode of Midsomer Murders.
In 2000, she made her stage debut as Elaine in Terry Johnson"s West End adaptation of The Graduate. She has worked at the Royal Court and Bush theatres, both in London.
In 2004, Punch played receptionist Elaine Denham on Doc Martin.
She left the television show The Class after appearing in eleven of the first 12 episodes. Punch starred in Woody Allen"s 2010 film, You Will Meet a Tall Dark Stranger. In August 2010, she appeared in British Broadcasting Corporation Two"s three part police comedy-drama Vexed alongside Toby Stephens.
In 2011 Punch appeared opposite Cameron Diaz in Bad Teacher, portraying sanctimonious school teacher Amy Squirrel.
Punch was cast as Deena Pilgrim, the female lead in the television pilot Powers for the Forex channel, but the role was recast.