Deller was born in Margate, a seaside resort in Kent. As a boy, he sang in his local church choir. When his voice broke, he continued singing in his high register, eventually settling as a countertenor. Throughout the 19th century, it was only in the tradition of all-male cathedral choirs that the countertenor voice had survived. Deller was himself successively a member of the choirs of Canterbury and St. Paul's Cathedrals (1940-47 and 1947-62, respectively). He emerged as a soloist from this choral tradition, largely due to the admiration of the composer Michael Tippett, who heard him while at Canterbury and recognized the unique beauty of his voice. Tippett introduced him to the public as a countertenor, rather than a male alto. He also became better known with a radio broadcast (on the BBC's new "Third Programme") of Henry Purcell's Come ye Sons of Art. He concentrated on popularizing and recording the music of English Baroque and Renaissance music by composers such as John Dowland and Purcell.
Deller's voice sounded remarkably high. Misconceptions about the countertenor voice were common at the time Deller was first gaining significant notice as a singer, which was only a matter of decades after the last castrati had died; Michael Chance tells the story that once, a French woman, upon hearing Deller sing, exclaimed "Monsieur, vous êtes eunuque"—to which Deller replied, "I think you mean 'unique,' madam.
He formed the Deller Consort in 1948, a group dedicated to historically informed performance. The group significantly expanded popular notions of the Baroque repertoire, producing high-quality authentic "period performances" of the works of Bach, Handel, Purcell, Dowland, and even folk songs; the membership of the consort changed over the years. It included soprano Mary Thomas and, from 1964, Deller's son, Mark Deller (Mr. Deller's other son, Simon, trained as a music teacher during the 1960s.) As well as directing the Consort, Deller also conducted some performances with chamber orchestras.
In 1960, Deller sang the role of Oberon in Benjamin Britten's opera A Midsummer Night's Dream. Britten wrote this role with Deller specifically in mind, although he was dropped from staged revivals of the work against the composer's wishes, probably because of poor acting technique. He did record the opera, with the composer conducting.
Lutenist Desmond Dupré performed with him, initially as a guitarist; other accompanists included harpsichordist and musicologist Walter Bergmann. In later years, he worked with lutenist Robert Spencer and harpsichordists Harold Lester and William Christie. His recordings include the lute songs of Dowland, operas by Handel, Britten's A Midsummer Night's Dream, songs and semioperas by Purcell (such as The Fairy Queen), traditional English folk songs, works by Thomas Tallis, and the Bach alto repertoire. He recorded for HMV, Vanguard Classics, and Harmonia Mundi.