Together they devised and wrote 1950s and 60s BBC sitcoms including Hancock's Half Hour (1954–1961), the first two series of Comedy Playhouse (1961–1963), and Steptoe and Son (1962–1974).

Galton was born in Paddington, West London, and after leaving school he worked for the Transport and General Workers Union.

He contracted tuberculosis aged 18 in 1948 and was admitted to Milford Sanatorium near Godalming in Surrey, where he met fellow patient Alan Simpson.

In October 2005, Galton and Antrobus premiered their play Steptoe and Son in Murder at Oil Drum Lane at the Theatre Royal, York.

The play was set in the present day and related the events that led to Harold killing his father, and their eventual meeting thirty years later (Albert appearing as a ghost).