In London in 1967, he studied with John Lambert, Alexander Goehr and Tristan Murail and first came to prominence when his orchestral Diptych (1990) won an RPS Prize in 1992. Anderson has held Composer in Residence positions with the City of Birmingham Symphony, Cleveland and London Philharmonic orchestras, relationships which produced an impressive body of orchestral works including Stations of the Sun (1998, a BBC Proms Commission) and Eden (2005, Cheltenham Festival). More recently, Fantasias (2009), written for the Cleveland Orchestra, won a British Composer Award and The Discovery of Heaven (2011), a co-commission by the New York Philharmonic and the London Philharmonic Orchestra was awarded a South Bank Sky Arts Award. Both works were recorded by the LPO live label.
Anderson has enjoyed commissions from bodies including the BCMG, London Sinfonietta, Asko-Schönberg Ensemble and Cheltenham Festival. Book of Hours for ensemble and electronics (2004) won the 2006 RPS Award for Large Scale Composition and featured on a NMC portrait disc. This was one of two recordings of his music to be nominated for a 2007 Gramophone Award, the other being the eventual winner, Alhambra Fantasy (Ondine). Poetry Nearing Silence (1997), originally a commission from the Nash Ensemble, was later arranged to become a successful ballet choreographed by Mark Baldwin. In 2009, Anderson and Baldwin collaborated again on a Darwin-inspired ballet, The Comedy of Change, which toured nationally.
Anderson has been particularly active in the world of choral music. His Four American Choruses (2003) were premiered at the Concertgebouw by the Netherlands Radio Choir and Bell Mass (2010) was written for the Choir of Westminster Abbey and James O'Donnell. In 2011, Anderson was a double winner at the British Composer Awards with Bell Mass winning in the liturgical category and Fantasias taking the orchestral prize. His 2006 oratorio Heaven is Shy of Earth (rev. 2009) premiered at the BBC Proms, was awarded the BASCA award for Choral Composition in 2007. Alleluia for choir and orchestra (2007) was written to open the newly refurbished Royal Festival Hall, whilst Harmony was commissioned for the First Night of the BBC Proms 2013.
Anderson's first opera, Thebans, with a libretto by distinguished playwright Frank McGuinness based on the Sophocles' Theban plays, premiered at English National Opera in May 2014 and received its German premiere in Bonn in May 2015.
Renowned as an enabler, teacher and programmer, Anderson has held senior professorships at the Royal College of Music, London (1996-2004, where he was Head of Department for five years) and at Harvard University (2004-7), and is currently Professor of Composition and Composer in Residence at Guildhall School of Music & Drama. Former students include Huw Watkins, Helen Grime, Ulrich Kreppein, Chris Trapani, Mark Simpson and Edmund Finnis. He was Artistic Director of the Philharmonia's Music of Today series from 2002 to 2011 and in 2012 he was appointed Vice President of the Conseil Musical de la Fondation Prince Pierre de Monaco.
From 2013-2016 Anderson was Composer in Residence at London's Wigmore Hall. Recent projects have included a Violin Concerto, 'In lieblicher Bläue', which was premiered by Carolin Widmann and the London Philharmonic Orchestra under Vladimir Jurowski in March 2015, and Van Gogh Blue (2015) for the Nash Ensemble. Incantesimi, a new work for the Berliner Philharmoniker and Simon Rattle will premiered in the summer of 2016.