Davies was born in Salford, Lancashire, the son of Thomas and Hilda Davies. At age four, after being taken to a performance of Gilbert and Sullivan's The Gondoliers, he told his parents that he was going to be a composer. He took piano lessons and composed from an early age. As a 14-year-old, he submitted a composition called "Blue Ice" to BBC Children's Hour in Manchester. BBC producer Trevor Hill showed it to resident singer and entertainer Violet Carson, who said, "He's either quite brilliant or mad". Conductor Charles Groves nodded his approval and said, "I'd get him in". Davies' rise to fame began under the careful mentorship of Hill, who made him the programme's resident composer and introduced him to various professional musicians both in the UK and Germany. After attending Leigh Boys Grammar School, Davies studied at the University of Manchester and at the Royal Manchester College of Music (amalgamated into the Royal Northern College of Music in 1973), where his fellow students included Harrison Birtwistle, Alexander Goehr, Elgar Howarth and John Ogdon. Together they formed New Music Manchester, a group committed to contemporary music. After graduating in 1956, he studied on an Italian government scholarship for a year with Goffredo Petrassi in Rome.

Seven Brightnesses (1978)