A session musician for many years, Wright frequently acted as arranger and "fixer" for recording sessions. He was a prolific jazz and orchestra composer. He led many bands, from small ensembles to night club bands to orchestras. He worked with Latin American and Jamaican bands, including Kenny Graham's Afro-Cubists and Mike McKenzie (jazz musician)'s Quartet. He played with the Carl Barriteau orchestra, the Decca Records house band under Phil Green, and occasionally the Glenn Miller band. Wright was voted the 1980 BBC Jazz Society Musician of the Year.