- Before becoming famous for his work in British television, Simpson was Margot Fonteyn's musical director.
- His distinctive music for television was often created using an ensemble of just a couple of horns, clarinet and bass clarinet, percussion and electric organ.
- He graduated in Composition and Pianoforte from Melbourne Conservatorium of Music. He was also qualified in Orchestration.
- His contribution to British television led director Michael Hayes to describe him as "the UK's answer to Bernard Herrmann".
- He was the first choice to compose incidental music for Doctor Who (1963) under three successive producers of the series: Barry Letts, Philip Hinchcliffe and Graham Williams.
- He died just two days after the director Paddy Russell, with whom he worked on three Doctor Who (1963) serials.
- His death was marked with a five minute tribute by Matthew Sweet on BBC Radio 4's Last Word.
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