Born in London, Pepperdine co-wrote and starred in the BBC Four sitcom Getting On with Jo Brand and Joanna Scanlan.

She has appeared in over 50 TV shows, including episodes of Rev, Midsomer Murders, Still Open All Hours, New Tricks, Doc Martin, Twenty Twelve, Lovesick, frequent collaborator Julia Davis' dark comedy Nighty Night, Jack Dee's Lead Balloon, Steve Coogan's I'm Alan Partridge and Mid Morning Matters, Saxondale, and Miranda Hart's Christmas Unwrapped and Miranda.

In 2014, Pepperdine played Harry Hill's housekeeper Mrs Flittersnoop in The Incredible Adventures of Professor Branestawm on BBC One.

[4] Her theatre work includes the role of Mrs Candour in Deborah Warner's 2011 production of The School for Scandal at the Barbican Centre.

In 2017 Pepperdine appeared in comedy feature Eaten by Lions alongside Antonio Aakeel and Jack Carroll, directed by Jason Wingard.