Davies was born in Salford, Lancashire. He grew up in Lancashire. He learned to play the piano and started composing when he was still very young. After education at Leigh Grammar School, he studied at the University of Manchester and at the Royal Manchester College of Music (now part of the Royal Northern College of Music). He met other students there who became famous musicians: Harrison Birtwistle, Alexander Goehr, Elgar Howarth and John Ogdon. Together they formed a group which they called the “New Music Manchester”. This group performed a lot of contemporary music (music that was being composed at the time). After a short stay in Rome he got a job as Director of Music at Cirencester Grammar School from 1959 to 1962.