Pepperdine's parents both worked in the NHS in south-west London (partly inspiring Getting On). Having studied history of art at the University of East Anglia, and having worked for Help the Aged and in publishing, at the age of 27 she applied to East 15 Acting School in Debden, because her heroine Alison Steadman had been there. She played a part in the first series of Doc Martin (2004).
Her theatre work includes the role of Mrs Candour in Deborah Warner's 2011 The School for Scandal at the Barbican Centre.
In 2014, she co-wrote, co-produced and starred in Puppy Love, again with Joanna Scanlan. She is an Executive Producer on HBO's change format series of "Getting On," and appeared as Dr Pippa Moore in one episode "Am I still me?" in season 3.
In December 2016, she was featured in the Christmas special of the Channel 4 comedy series The Windsors as Princess Anne. She reprised this role in the second series of the show.
It was announced in May 2017 Pepperdine would appear in comedy feature Eaten by Lions alongside Antonio Aakeel and Jack Carroll, directed by Jason Wingard.
