While growing up in Biloela, Brown played piano, wrote poetry, painted, as well as performing small stage pieces at the local theatre.

He subsequently undertook tertiary studies at the University of Queensland (UQ) to be a history and geography teacher,[6] and while doing so, became involved with the student drama company Dramsoc.

[8] Brown's career took him abroad to Britain, where he joined the Royal Shakespeare Company (RSC), and was the first Australian commissioned to write and perform in their own play The Swan Down Gloves.

He appeared in the RSC's premiere production of The Wizard of Oz in the roles of the Wicked Witch of the West and Miss Gulch, for which he was nominated for an Laurence Olivier Award in 1988.

Brown made his Broadway debut as an actor in 1986 in Michael Frayn's Wild Honey with Ian McKellen, directed by Christopher Morahan, and as a playwright with his adaptation of a benefit performance of A Christmas Carol in 1985, featuring Len Cariou as Scrooge.

In 1999 he also had major success throughout Australia as Oscar Wilde in the Belvoir St production of David Hare's The Judas Kiss, for which he won a Matilda Award.

In 2012, he performed to critical acclaim as Bruscon in sell-out seasons of Thomas Bernhard’s play The Histrionic in both Melbourne and Sydney,[14] receiving a Helpmann Awards nomination.

John Cleese cast Brown in 1997 film Fierce Creatures (the sequel to A Fish Called Wanda), after spotting him performing onstage at Stratford in the UK.

Brown appeared in several other films, including Oscar and Lucinda (1997) as Percy Smith, The Dish (2000) as the Prime Minister, The Chronicles of Narnia: The Voyage of the Dawn Treader (2010) as Coriakin, Killer Elite (2011) as Colonel Fitz and Singularity (2013) as Egerton.

[18] In 1999 he accepted an offer to be Adjunct Professor in the School of English, Media Studies and Art History at the University of Queensland, and gave workshops and master classes for drama students.