Blakiston was born in Chelsea, London and attended the Royal Academy of Dramatic Art.
Blakiston's first notable role was in The Avengers. She starred in three episodes from 1961 to 1967. She appeared to great acclaim in the BBC adaptation of The Forsyte Saga in 1967. She then played Lady Patience Hardacre in Brass from 1983 to 1990.
Blakiston was married to Russell Hunter from 1970 until they divorced. They have two children.