As a chamber musician, Barnaby has performed and recorded much of the clarinet, violin and piano repertoire with the Zanfonia Trio, BBC Music Magazine praised their most recent recording as a 'fine disc…leaving me hungry to hear more'. He also performs regularly with London Winds, Belcea Quartet, Thomas Adès, Conchord Ensemble, Artur Pizarro, OAE Wind Soloists, Endymion Ensemble and the Philharmonia Soloists. Barnaby has recorded chamber repertoire for ASV, BBC, Black Box, EMI and broadcasts regularly on BBC Radio 3 & Classic FM.

He has performed the Mozart Clarinet Concerto on both modern and period instruments and recorded as a soloist for Decca and with the Philharmonia Orchestra, Spohr Clarinet Concertos and for the Miramax film With or Without You.

Barnaby has worked with orchestras including the Academy of Ancient Music, Academy of St Martin in the Fields, Chamber Orchestra of Europe, ENO, Glyndebourne Touring Opera, London Chamber Orchestra, London Sinfonietta, London Symphony Orchestra, Orchestra of the Age of Enlightenment, Royal Opera House Orchestra, Royal Philharmonic Orchestra and the Scottish Chamber Orchestra. He was appointed Joint Principal Clarinet of the Philharmonia Orchestra in March 2000.

Barnaby is Professor of Clarinet at the Guildhall School of Music, the Royal College of Music and the Royal Northern College of Music.

The Philharmonia's Principal Clarinet's Chair is endowed by the Philharmonia Orchestra and Friends of the Philharmonia Orchestra in memory of Clem Relf.