He had early success with a series of recordings in which he set the poems of the British Poet Laureate Sir John Betjeman to music; Banana Blush, Late Flowering Love (both 1974), Sir John Betjeman's Britain (1977) and Varsity Rag (1981).
The albums, in which the poet recited his own words and the composer conducted a small group of musicians, have continued to be held in high regard by listeners and critics.
[4][5] These and subsequent records, including Captain Beaky and His Band, with words by Jeremy Lloyd, which topped the charts as both a single and album, led to work in television as well as in London West End theatres, where Parker had three musicals produced.
Parker won the British Academy Award for Best Original Television Music four times, and wrote scores for over two hundred programmes.
His work in film and television ranged from music for Moll Flanders, Tom Jones, Midsomer Murders, Born and Bred, Foyle's War, The House of Eliott, and Mapp & Lucia to the score for the contemporary political thrillers House of Cards (UK version), To Play the King and The Final Cut.