Cooke was educated at The Downs School in Wraxall, Somerset, Harrow School and Christ Church, Oxford.
He served as a councillor on Bristol City Council 1954-1957 and was a teacher of English at a Bristol public school. While a councillor and teacher, Cooke contested Bristol South East in 1955. He introduced the Fatal Accidents Acting 1959, the direct forerunner to the Fatal Accidents Acting 1976 which provides for investigation and compensation in cases of work-related deaths.
Cooke died in January 1987 at the age of 56 of Motor Neurone Disease.
He was the owner of Athelhampton House in Dorset, location of the 1972 film Sleuth, starring Michael Caine and Laurence Olivier, as well as the 1976 Doctor Who serial The Seeds of Doom.
41st United Kingdom Parliament. 42nd United Kingdom Parliament. 43rd United Kingdom Parliament.
44th United Kingdom Parliament.
45th United Kingdom Parliament. 46th United Kingdom Parliament.
47th United Kingdom Parliament]
He was Member of Parliament for Bristol West from a 1957 by-election until 1979.