Morgan is currently the violist of the Kreutzer String Quartet, the Locrian Ensemble and the Gavin Bryars Ensemble, with whom he records and travels extensively throughout Europe, and the world. He was a founder member of the Solaris String Quartet specialising in the music of composers interned in the Terezin concentration camp, Czechoslovakia, during the second world war. He has worked with many composers in England, Europe and Australia. Composers including Michael Finnissy, David Matthews, Jeremy Dale Roberts, Judith Bingham, David Gorton and Gloria Coats have all written quartets for the Kreutzer Quartet.
He has a busy recording schedule. He features as a solo artist on Naxos, and has recorded both Solo and as a chamber musician for Naxos, Dutton Epoch, GB Label, Toccata Classics, Guild, ABC Classics, BMS, NMC, and Metier.