He was born Harry Parr Davies in Briton Ferry, Neath, South Wales and was a musical prodigy, having composed whole operettas by the time he was in his teens. He came to the attention of composer Sir Walford Davies, who encouraged him to study at Oxford. At the age of fourteen he had already composed six songs, and left Wales to expand upon his juvenile success.
From 1934, he worked as accompanist for Gracie Fields. He wrote songs for Jack Buchanan and Anna Neagle among others. His best-known songs included "Pedro the Fisherman", "Wish Me Luck as You Wave Me Goodbye" and "Sing as You Go".
In 1939 the show Black Velvet included Parr-Davies's song "Crash, Bang, I Want To Go Home". Other wartime shows which featured his work included Big Top, Happidrome (starring Tessie O'Shea), Full Swing, The Knight was Bold and The Lisbon Story. In the course of the war he was seconded from his regiment to join Gracie Fields in ENSA.
In 1944, his musical, Jenny Jones, which had a Welsh setting, was a flop, but it was followed by the successful revue Fine Feathers (1945), Her Excellency (1949) starring Cicely Courtneidge, and Dear Miss Phoebe (1950).
Parr-Davies was at the peak of his success when he died of a perforated ulcer, for which he had declined to seek medical attention.
Songs by Parr-Davies used in George Formby films
- "Bell Bottom George" (Park/Parr-Davies)
- "If I Had a Girl Like You" (Park/Parr-Davies)
- "In My Little Snapshot Album" (Harper/Haines/Parr-Davies)
- "It's in the Air" (Parr-Davies)
- "Noughts and Crosses" (Hunter/Parr-Davies)
- "Swim Little Fish" (Park/Parr-Davies)
- "Your Way Is My Way" (Parr-Davies)