Outram attended Cambridge University and the Royal Academy of Music, studying viola with John White. In 1984, he began teaching at the Royal Academy of Music and has remained in that position. Four years later, he became a founding member of the Maggini Quartet. This group has toured widely in Europe, North America, and Asia, but has perhaps been best known for its recordings of works by British composers, including a complete cycle of the ten Naxos Quartets of Peter Maxwell Davies. Outram has also performed and recorded as a concerto soloist and in duo sonata repertory, again focusing on British music. He is a specialist in the viola music of Arnold Bax, himself a violist, and he has performed unusual repertory such as the Romanza of composer Elizabeth Maconchy, and concertos by David Gow and Adam Gorb. Principal violist of the Britten Sinfonia Soloists Ensemble, Outram won the Royal Philharmonic Society Award for Chamber Music in 2009.
Outram's more than 40 recordings with the Maggini Quartet include several that have won major British recording industry awards, and his album English Viola Sonatas, recorded with pianist Julian Rolton, received a five-star rating from BBC Music. In 2019, with Rolton and tenor Mark Padmore, he released a recording of Vaughan Williams' Viola Fantasia.
Outram's activities at the Royal Academy have included scholarship as well as performance teaching; his editions and arrangements of music by Delius, Britten, Ireland, and others have been published by such houses as Boosey and Hawkes, Stainer and Bell, and Comus. Among his research interests is 19th century viola pedagogy. ~ James Manheim, Rovi