In 1989, he and a fellow Lay Clerk at Christ Church, Andrew Carwood, founded a vocal ensemble which they named The Cardinall's Musick. It was devoted to music of the Catholic English composers of the pre-Reformation. In 1991, the ASV record company asked the group to sing the music of Nicholas Ludford on their Gaudeamus early music specialty imprint label, which led to a four-disc series of that composer's complete music.
While Carwood performed more of the conducting tasks, Skinner undertook the group's research. Their performances and recordings are all based on newly prepared editions by Skinner, who goes back to the original manuscripts or the printed editions prepared during the composers' lives.
He has sung with a number of the leading specialist early music ensembles. He is also a record producer, who has made discs with The Exon Singers, the Brompton Oratory, Cambridge Taverner Choir, and the Binchois Consort, and produced music for the ASV, Hyperion, Herald, and EMI labels. He has also prepared new editions of music for performance and recordings by The Tallis Scholars and The Sixteen.
Skinner is a member of the Committee of the Plainsong and Medieval Music Society.
He began a project to prepare the Early English Church Music edition of the complete music of Ludford and has published widely on the subject of music and the Reformation in the English Collegiate Churches.
He is a Postdoctoral Fellow of the British Academy at Christ Church and a lecturer in music at Oxford University. He frequently gives master classes on music history and singing from early music notation in the United Kingdom and abroad. His work with The Cardinall's Musick has won the Gramophone Award for Early Music, the French Diapason d'Or, the German Schallplattenkritik Preis and the Schallplatten Echo Award.