Barnaby was, and still is, part of a family of artists and musicians; his father Bryan Southcombe had a brief stint as an actor, and his mother is one of the most celebrated movie actresses working in Europe. Barnaby's step-father is Jean Michel Jarre, the famous French musician who was married to Barnaby's mother Charlotte Rampling for over 20 years. Jean Michel Jarre's father was Maurice Jarre, the Hollywood composer. Barnaby's half brother David Jarre is a magician, and his half sister Emilie Jarre is a model and fashion designer. His step-aunt Stéfanie Jarre is a production designer in movies and TV.

Son of Charlotte Rampling and Bryan Southcombe .Has a half-brother named David Jarre (b. 1977), a magician.