After his voice changed to tenor, he was accepted as a lay clerk at St. Alban's Abbey -- in other words, he was a paid member of its choir. He studied at the Royal College of Music in London with John Birch as his organ teacher, with vocal studies under Ruth Packer and Wilfred Brown. He received diplomas and a prize from the RCM for his organ playing, and the Bachelor of Music degree from London University. Although he has worked as an organist, his distinctive talents as a singer led him to make his career with his voice.
Covey-Crump is a "tenor haute-contre," a natural voice in a high range without falsetto, while still retaining the characteristic ring of a true tenor. His example has led to a revival in singing certain music by tenors, which the New Grove Dictionary's article on him by George Pratt concludes is "a major contribution."
His vocal type and his interest led him to the early music movement rather than to the traditional art song repertory or the operatic stage. The list of early music ensembles with which he has sung is virtually a history of the London early instrument movement since the mid-1960s and includes David Munrow's Early Music Consort, the Consort of Musick, the Medieval Ensemble of London, the Landini Consort, the Deller Consort, the Taverner Consort, the Baccholian Singers, the King's Consort, and the Washington, D.C. based Folger Consort. In 1981, he was one of the founders of Gothic Voices.
Much of his activity is devoted to his membership in the Hilliard Ensemble. This ensemble of four voices (five since 1999) performs up to 100 concerts and conducts its own summer school and festival. (For several years based in Cambridge, the Hilliard shifted to Germany in 2000.)
Covey-Crump is far from being exclusively interested in older music. As a member of Songcircle he participated in the first performances and recording of Stimmung (Voices) by German avant-gardist Karlheinz Stockhausen. Particularly in recent years (since they formed an association with the exploratory record label ECM) the Hilliard Ensemble has often sung very recent and experimental music by the likes of Arvo Pärt and Jan Garbarek. Covey-Crump also frequently sings in such repertory as Handel oratorios and the major J.S. Bach choral masterpieces. He is known as one of the leading Evangelists in the Bach Passions. His appearances in the Passions with Denys Darlow at St. George's Church, Hanover Square, has become virtually a Good Friday tradition. He is also active as a solo singer with a repertory extending from Renaissance lute-songs, Baroque, the Classical era, and contemporary music. He is especially known for his performance of music of Henry Purcell. He has made over a dozen Purcell recordings for the Hyperion label.
From his days as an organist he took an interest in the history and practice of various musical temperaments (tuning systems) used from early times to the present. He has published several articles on that subject as applied to vocal music and his accurate pitch and ability to adapt to different temperaments is a major factor in his outstanding career.