John Straffen's father, John Straffen Sr, was a soldier in the British Army. The younger Straffen was the third child in the family; his older sister was regarded as a "high grade mental defective" who died in 1952. Straffen was born at Bordon Camp in Hampshire where his father was then based. When Straffen was two years old, his father was posted abroad and the family spent six years in India. Returning to the UK in March 1938, Straffen's father took a discharge from the Army, and the family settled in Bath.