Graham is cellist of four chamber ensembles which reflect his diverse musical tastes.

The Farrington Ensemble, with Iain Farrington (piano), Peter Sparks (clarinet) and Tom Hankey (violin), has had considerable success performing in various UK festivals and a range of other venues. Founded to perform Messiaen's Quatuor, and with repertoire ranging from piano trios and clarinet trios to contemporary music and arrangements for the whole group, the ensemble prides itself on its friendly approach and flexible programming.

Graham has recently joined Janiculum, a group established by the harpsichordist Jane Clark, which performs little-known works from the middle- to late-eighteenth century. Its repertoire consists of the kind of music with which audiences at the time would have been familiar, but which has since fallen into obscurity. The group has recorded six CDs, which are available on their website.

Classico Latino, with Ivan Guevara-Bernal (piano) and Lizzie Ball (violin), is a group performing classic Latin-American popular music. Since its formation in Cambridge in 1998, Classico Latino has performed throughout Europe and Scandinavia, and, following a hugely successful tour of Colombia, has been offered a major recording contract.

The British Camerata, with Julian Perkins (harpsichord), Alex Ashworth (baritone) and others, is an early-music ensemble which reached the final of the 2005 York Early Music Competition. Performing a wide range of vocal and instrumental music, it focusses on French and Italian Cantatas of the Baroque era.