Anthony has narrated many TV documentaries including Secret Lives and Secret History. His voice has been heard in advertisements for Tesco and Orange.
Anthony is the winner of both a Sony award and a Radio Times award for his radio performances. In 1995 on BBC Radio 4 he played Stephen Maturin in Patrick O'Brian's Master and Commander, dramatised by Roger Danes and directed by Adrian Bean. Recent radio projects[when?] include the much praised "Life and Fate" for BBC Radio 4 with Kenneth Branagh and Harold Pinter's version of "The Heat Of The Day" with Anna Chancellor.
In 2011, Anthony played Evelyn Waugh, opposite Fenella Fielding as Nancy Mitford, in the sell-out production of "Dearest Nancy...Darling Evelyn" at the Jermyn Street Theatre, London.