Hope was born in Kettering, Northamptonshire and bought up in Norfolk. Hope attended Oakham School from 1967-1971 and then studied law at Notthingham Trent University.
Hope trained at the National Youth Theatre from 1972-76 where he appeared in several new plays by established writers.
In 1976 he joined the NYT’s professional Dolphin Theatre Company where he starred in Romeo and Juliet.
He then won a role in the first stage production of The Hitchhiker's Guide to the Galaxy with Ken Campbell’s The Science Fiction Theatre of Liverpool. He also appeared in their 22-hour epic The Warp and The Third Policeman. Hope made his first West End appearance with Le Grand Magic Circus in 1001 Nights at the Shaftesbury Theatre in 1980.
In 1981, Peter Gill cast him in Much Ado About Nothing which started his long association with The National Theatre.
In 1996, he appeared as Pierre Bezukhov in the Shared Experience production of Leo Tolstoy's War and Peace at the National Theatre, and then Levin in the Shared Experience production of Anna Karenina. Hope was Associate Director of the production.
With Mark Rylance he was one of the six actors in Mike Alfreds’ Cymbeline at Shakespeare's Globe Theatre in 2001. In 2002, the Royal National Theatre staged an adaptation of John Irving’s A Prayer for Owen Meany.
Hope played Max Kellerman in Dirty Dancing at the Aldwych Theatre in 2010. He then returned to the Almeida Theatre as Gabriel York in Andrew Bovell’s When the Rain Stops Falling in 2009 and in 2012 as Albany in King Lear with Jonathan Pryce.
He plays recurring characters in Doctor Who. Since 2015, he has portrayed Harris Pascoe in the 2015 BBC adaptation of Poldark.