Parrott and the Taverner groups have built one of the leading reputations in Baroque and pre-Baroque music. They appeared at the 1977 Promenade Concerts in London in Monteverdi's Vespers and were the first to give a period instruments performance in London of Bach's Mass in B minor. Parrott's career includes substantial work researching, writing, and lecturing on early music. His The Essential Bach Choir was published in 2000, and he was co-editor of the New Oxford Book of Carols. His activities also include a substantial amount of performing later repertory and has expanded to a sizeable involvement in opera. He has appeared with the Orchestra of the Age of Enlightenment, and has a close relationship with the Slovak Philharmonic and the Residentie Orchestra of The Hague. In 1989 he became artistic director of the Kent Opera and has conducted at La Scala, the Royal Swedish Opera at Drottningholm, and the Royal Opera House at Covent Garden, London. He is an active conductor of modern music, including works of Tippett, Tavener, Nono, Varèse, Britten, and Stravinsky, and premiered Judith Weir's A Night at the Chinese Opera. In 2000, he was named musical director and principal conductor of the London Mozart Players and in 2002 took on the same positions with the New York Collegium.
Before becoming an exclusive Sony Classics artist, Parrott recorded on the L'Oiseau-Lyre and Hyperion labels and on the EMI Reflexe and Virgin Veritas labels.