Born in Melbourne to Henry William Crawford (a commercial salesman) and Charlotte Tuner (a contralto and organist), Hector Crawford studied at the Melbourne Conservatorium of Music, where he was also the conductor.
In 1940, he joined the Broadcast Exchange of Australia as its he became the musical and recording director: by 1942, he was its managing director in 1942. In 1944, his sister Dorothy, who had been working at the Australian Broadcasting Commission (ABC) as an announcer, joined him at the Broadcast Exchange of Australia.
In 1945, the siblings co-founded Hector Crawford Productions (later simply Crawford Productions), as a producer of radio dramas and serials. While Dorothy specialised in script-editing and casting, Crawford managed music, sales and administration.
With both Crawford and Dorothy having a strong background in music, their early productions were often music based, including the Concerts for the People: live concerts in the Melbourne Botanical Gardens, often conducted by Crawford and broadcast live on radio.
In 1961, with Consider Your Verdict, Crawford Productions began what was to be a domination of Australian television programming over the next two decades.
In the 1970s, Crawford was heavily involved in the Make It Australian campaign, which pushed for locally produced content on Australian television. He was made a member of the Australian Film and Television School in 1973 and of the Australian Film Commission in 1974, both appointments occurring under the auspices of the Whitlam Government.
Crawford sold his controlling interest in Crawford Productions in 1987, and retired in 1989.