Emsley initially studied with Arnold Whittall at University College, Cardiff, after which he moved to London, where he still lives. He attended Peter Maxwell Davies' composition classes at the Dartington Summer School of Music, and co-founded the Cardiff Composers' Ensemble while a student there. In the 1970s he co-founded, with James Clarke, the ensemble Suoraan, which specialised in performances of music by contemporary composers, including Iannis Xenakis, Michael Finnissy and James Dillon.
In addition to composing, Emsley works as a music engraver. He was the first ever user of the notation software Sibelius, having tested it extensively before it was released, and engraved the first score published using Sibelius: Antara by George Benjamin (published by Faber Music).