Born in Yorkshire, Blythe studied drama on scholarship at the Royal Academy of Dramatic Art after serving in the Royal Air Force. He began his professional career as a repertory player with the Living Theatre Company, the Nottingham Playhouse, and the Royal Shakespeare Company. He made his West End debut in 1965.
Blythe was frequently associated with the director Peter Hall and the playwright Alan Ayckbourn.
Blythe worked on film only rarely and usually in minor roles; his most substantial part was also in his last film appearance, The Luzhin Defence (2000). Other film credits include two movies for Hammer Film Productions, A Challenge for Robin Hood and Frankenstein Created Woman; his most successful film was Carrington (1995).
By contrast, Blythe appeared in several dozen television series, miniseries, and movies, most notably as Samuel Ballard, QC in Rumpole of the Bailey (1983-92). He guest-starred in episodes of The Avengers, UFO, Callan, New Scotland Yard, Special Branch, Agatha Christie's Partners in Crime, Poirot, Inspector Morse, Maigret, The Inspector Alleyn Mysteries, Between the Lines, Pie in the Sky, Goodnight Sweetheart, Dalziel and Pascoe, and Foyle's War (aired posthumously), among many others. His miniseries appearances included Barchester Towers, After the War, and The Alan Clark Diaries.
One of Blythe's plays, Tom, Dick, and Harry, was produced at Theatre in the Round in 1972. He also wrote two poetry chapbooks, Spring and The Light.
Blythe lived for eight years with Harriet Walter; the two were planning to marry at the time of his death.
