Cave's musical training began as a chorister at the age of seven, leading to studies at Oxford University under Simon Preston and David Wulstan and a career performing as soloist and with ensembles including the Clerkes of Oxenford, The Tallis Scholars and the Choir of New College, Oxford.

Cave’s approach to early music is fuelled by curiosity and imagination, whether through the restoration of unknown or neglected works, or the reexamination of the familiar. He emphasises (actually, obsesses about) phrasing and textual expression, and with his background as a singer, encourages the use of vocal colours, timbres, and both bold and subtle nuances.

Now based in the USA, Cave directs choral ensembles at Duke University Chapel and is Executive Director of Chorworks, a non-profit organisation that provides singers and conductors with the opportunity to study and perform choral music from the sixteenth and seventeenth centuries. He lives in Chapel Hill, North Carolina, and is still trying to understand the difference between a biscuit and a scone.