As well as being a jazz flautist, Parker is a multi-instrumentalist and often plays keyboards during live performances and workshops.
He was a founding member of and composer for the British jazz band Loose Tubes in the 1980s. Since then, he has toured and performed with several noted bands and performers including Bheki Mseleku, Marvin Smith and John Parricelli. He currently tours with his present band Mister Vertigo, of which Parricelli is also a member, and conducts various jazz workshops and performances involving young musicians across the country. He was a lecturer in jazz at Middlesex University, where he lectured, among other, musicians from Led Bib.