- The composer's two elder brothers were also called Clifton Parker: Arthur Dennis Clifton Parker (1899 - 1967) James Dennis Clifton Parker (1901 - 1944)
- Father of Roselyn Ann Clifton Parker (Usually credited as _Roselyn Parker_).
- Notable theatre scores included Tolstoy's 'War and Peace', staged at the London Phoenix from August 6 to 21, 1943. Muir Mathieson conducted the London Symphony Orchestra.
- Notable radio scores included Alan Burgess's 'The Passing of Crab Village' broadcast on the Home Service on 24 September 1950. Muir Mathieson conducted the BBC Orchestra.
- Parker's work as war documentary composer was honoured at the Imperial War Museum during June and July 2003 with special screenings of Battle Is Our Business (1942), Towards the Offensive (1944) and Western Approaches (1944).
- The Clifton Parker Bursary was established at Dartington International Summer School in Devon to assist young composers study film music.
- Father of Julia Clifton Parker, better known as writer Julia Stoneham.
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