Her leading roles have included You, Me and It (1993), A Mind to Murder (1995),The Vet (1995–96), the children's series Microsoap (1998–2000).
She played Rebecca Plunkett in Midsomer Murders "A Talent for Life" (2003) and Sarah in Fear, Stress and Anger (2007).
At the Chichester Festival Theatre, in the 2006 season, she played Lydia Cruttwell in Terence Rattigan's In Praise of Love and the following year, she was Maria in Twelfth Night and Lady Macduff in Macbeth.
[2] Burden appeared in Black Mirror: Bandersnatch, released on Netflix on 28 December 2018.
Burden has also co-starred in several radio dramas for BBC, along with Bill Nighy, in Simon Brett's comedic murder mystery series Charles Paris.