Punch was born in Hammersmith, London. Her parents run a market research company. Punch was educated privately at Godolphin School and then Latymer Upper School. Punch performed with the National Youth Theatre from 1993 to 1997, and began a course at University College London before dropping out to become an actress.
Punch made her debut in a 1998 episode of The New Adventures of Robin Hood. Her other TV credits include the naive daughter of Alison Steadman's character in the short-lived series, Let Them Eat Cake that starred French and Saunders. She starred as a football player in the kids TV show Renford Rejects.
In 2004, Punch played the cheeky, kooky receptionist, Elaine Denham, in the television show Doc Martin.
She left the television show The Class after appearing in all but one of the first 12 episodes.
Punch starred in Woody Allen's 2010 film You Will Meet a Tall Dark Stranger, having replaced Nicole Kidman.In August 2010, she appeared in BBC Two's three part police comedy-dramaVexed alongside Toby Stephens.