Midgley married, first, the playwright and psychotherapist Liane Aukin, and, in 1991, the dancer and choreographer Denni Sayers.
After Cambridge, Midgley was employed as a drama producer for BBC Radio and was posted to Jamaica, where he worked closely with the comedian and broadcaster Charles Hyatt.
Midgley’s first London stage production, Kill Two Birds, was at the St Martin's Theatre in 1961, and his first in New York City, Those That Play the Clowns, in 1966.
Musicals of note included Joseph and the Amazing Technicolour Dreamcoat, produced several times at the Haymarket, in 1974, 1975, 1976, 1978, and 1985.
This became a great favourite with audiences and was developed at the Haymarket from its first shorter, school's version into the full-blown musical we know today.