In 1982, Meyer and his brother played the Poulencs in Peter Greenaway's The Draughtsman's Contract. Meyer played the assassin Mischka, a circus performer with a talent for knife throwing alongside his twin brother (Grischka) in the 1983 James Bond film Octopussy. He was credited as "Twin One". In 1985, Meyer appeared as Lysander in another Celestrino Coronado adaptation, in a television film production of Shakespeare's A Midsummer Night's Dream. He also portrayed the roles of Moth and Demetrius later in his career in the same play in Peter Brook stage productions. David and his brother turned down an opportunity to play Siamese twins in a performance at the Everyman Theatre in Liverpool in the mid 1980s.
