He is remembered along with his brother, William Paxton (1737–1781), for the composition of numerous pieces for the cello, most notably glees. Due to imprecise attribution methods of the time, the works of the two brothers are often confused or improperly attributed.
Paxton won London Catch Club prize medals for his glees How Sweet, How Fresh (1779), Round the Hapless (1781), Ye Muses Inspire Me (1783), and Blest Pow'r Here See (1784).
- Cansick, Frederick Teague (1869). A collection of curious and interesting epitaphs copied from the monuments of distinguished and noted characters in the ancient church and burial grounds of Saint Pancras, Middlesex,. 1. J.R. Smith.
- Robins, Brian (1998). The John Marsh journals: the life and times of a gentleman composer (1752-1828). Pendragon Press.
- Stevens, Richard John Samuel; Argent, Mark (1992). Mark Argent, ed. Recollections of R.J.S. Stevens: an organist in Georgian London. SIU Press. ISBN 0-8093-1790-7.
- Robins, Brian (2006). "Appendix B". Catch and glee culture in eighteenth-century England. Boydell Press. ISBN 1-84383-212-7.