Born on 15 May 1863 at 77 Copperas Hill, Liverpool, Lancashire, Hornby was the son of John Oswald Hornby, a provision merchant and his wife Martha Hornby (née Thomlinson), though this date has been questioned. It is the date on his birth certificate, but the entry in the family bible in his mother's handwriting gives the date as 2 May. At the age of sixteen, Hornby left school and started working as a cashier in his father's Business. On 15 January 1887 he married a schoolteacher Clara Walker Godefroy, the daughter of a customs officer and they had two sons, Roland and Douglas, and a daughter, Patricia. When his father died in 1899, his father's Business was closed and Hornby became a bookkeeper for David Hugh Elliot who ran a meat importing Business in Liverpool.