Francis Webb was born in Adelaide. His father was a musician, Director of the North Sydney Academy of Music before moving to Adelaide where he became the owner of a piano importing business in Grenfell Street. His mother was a socialite with a keen interest in horse racing. She died when he was two years old, and his father was hospitalised a year later. In 1928, Webb and his three sisters (Mavis, Claudia, and Leonie) were sent to live with their paternal grandparents, Charles and Amy Webb-Wagg, in Sydney.