After Robinson had his childhood in Broadstairs, Kent spent, he graduated from London's Central School of Speech and Drama. He made his debut as an actor in the movie Romeo and Juliet (1968 ) by Franco Zeffirelli. In the film Tchaikovsky - Genius and Madness (1970 ), he starred opposite Richard Chamberlain in the movie The Story of Adele H. (1975 ) by François Truffaut alongside Isabelle Adjani.
For the screenplay of the film The Killing Fields - Crying Country (1984), Robinson was nominated for film awards Oscar and Golden Globe and won the British Academy Film Awards ( BAFTA ) and the Writers Guild of America Award.
As a screenwriter, he won the Evening Standard British Film Award for the film Withnail & I (1987 ), in which he also directed. For the film, Jennifer 8 (1992 ) with Andy Garcia and Uma Thurman, he won a prize from the Cognac Festival du Film Policier.
After a long retreat from the film business in 2011, his film The Rum Diary, a Hunter S. Thompson adaptation starring Johnny Depp was in the lead role.
Robinson is married and has two children.