Cooke was born in Leicester to a poor, working-class family; his father died when he was a child, but his mother was able to afford piano lessons.
From Wyggeston Grammar School for Boys he won an organ scholarship to Selwyn College, Cambridge, where he was taught by Patrick Hadley and Robin Orr.
His job involved writing and editing scripts for the music department and broadcasting for radio and television, where his thoughtful, unaffected manner made him an ideal communicator.
Originally a lecture demonstration broadcast by the BBC in 1960, the first full (continuous) version was premièred on 13 August 1964 at the Proms by the London Symphony Orchestra under the baton of Goldschmidt.
During the final years of his life he had worked on a large-scale study of Wagner's massive operatic tetralogy Der Ring des Nibelungen.