McCallum's father, John Neil McCallum Sr., was a theatre owner and entrepreneur, who built and for many years ran the 2,000 seat Cremorne Theatre on the banks of the Brisbane River. After emigrating from Scotland, McCallum Snr. became an accomplished musician, and was soon heavily involved in Brisbane's entertainment scene. His mother was an accomplished amateur actress who was born in England.

In 1918, McCallum Jr. was born in Brisbane during the opening night of a comedy performance. After his birth, a family friend sent his father a wire: 'Congratulations on two howling successes'.