Campbell attended St Peter's School, Seaford and Uppingham School. At the outbreak of the Second World War he volunteered for the Royal Air Force, but was unable to serve because of a case of childhood rheumatic fever. He joined Briggs Motor Bodies Ltd in West Thurrock, where he became a maintenance engineer. Subsequently, he was a shareholder in a small engineering company called Kine Engineering, producing machine tools. Following his father's death on New Year's Eve, 31 December 1948 and aided by Malcolm's chief engineer, Leo Villa, the younger Campbell strove to set speed records first on water and then land.