Rees studied art in London and was "discovered" while working as a scene painter at Wimbledon. Within three years, he had joined the Royal Shakespeare Company and appeared in numerous productions there before winning international stardom as "Nicholas Nickleby". Post-"Nickleby" roles include the lead in Tom Stoppard's "The Real Thing" (1983), "Hamlet" (1984) and Stoppard's "Hapgood". In addition to acting, he has written and directed for the stage.
Rees has had a sporadic film career. He made his debut in Stephen Frears' "Saigon - Year of the Cat" (1983), adapted from David Hare's play. In Bob Fosse's "Star 80" (also 1983), he portrayed a film director loosely based on Peter Bogdanovich. Rees was sculptor Edgar Papworth in Bob Rafelson's biopic of explorers Sir Richard Burton and John Hanning Speke, "Mountains of the Moon" (1990). He turned villainous in both "If Looks Could Kill" (1991) and "Stop! or My Mom Will Shoot" (1992). For Mel Brooks' "Robin Hood: Men in Tights" (1993), Rees offered a spirited spoof of Alan Rickman's portrayal of the Sheriff of Nottingham in "Robin Hood: Prince of Thieves" (1991). He next appeared in Adrienne Shelley's feature directorial debut "Sudden Manhattan" and the film version of Jon Robin Baitz's "The Substance of Fire" (both 1996).