Barrett was born in Swansea, Wales. He began to study music seriously only after graduating in genetics and microbiology at University College London in 1980 (Warnaby 2001). From then until 1983 he took private lessons with Peter Wiegold. There followed fruitful encounters at the 1984 Internationale Ferienkurse für Neue Musik with Brian Ferneyhough and Hans-Joachim Hespos. In the 1980s he became associated with the so-called New Complexity group of British composers because of the intricate notation of his scores. However, he is equally active infree improvisation, most often in the electronic duo FURT with Paul Obermayer, formed in 1986, and a voice/electronics duo with Ute Wassermann since 1999, but also since 2003 as a member of the Evan Parker Electro-Acoustic Ensemble. Since 1990 about half of his compositions have been written for the ELISION Ensemble, most notably the extended works Opening of the Mouth, DARK MATTER,CONSTRUCTION and world-line. In 2005 he and Obermayer formed the electroacoustic octet fORCH.
He taught composition at Middlesex University from 1989 to 1992, and electronic composition at the Institute of Sonology of the Hague Royal Conservatory in 1996, where he taught until 2001. In 2009 he resumed teaching regularly at the Institute. Having moved from London to Amsterdam in 1993, he lived in Berlin from 2001 to 2013, initially as a guest of the DAAD's "Berliner Künstlerprogramm", except between 2006 and 2009 when he was a professor of composition at Brunel University in London (Service 2005). He is currently based in Belgrade.
Many of Barrett's works are grouped into series, and have extra-musical associations—particularly with the writers Samuel Beckett and Paul Celan, but also the Chilean painter Roberto Matta, and ideas from physics, mythology, astrology and philosophy (in the texts of DARK MATTER). Barrett's compositional techniques, which derive equally and indistinguishably from serial, stochastic and intuitive methods, have since the mid-1980s made extensive use ofCOMPUTER PROGRAMS he has developed himself (Warnaby 2001; McAuliffe 2014). He regards free improvisation as a method of composition rather than as a different or opposed kind of musical activity (Gilmore 2009). He has often been politically outspoken (Whittall 2005), and in 1990 joined the Socialist Workers Party. While no longer an active member he remains aligned with revolutionary socialism (Lenz 2005).
His codex series of compositionsEXPLORES diverse ways of using composed frameworks as a point of departure for improvisation, particularly with larger groups, while the fOKT series extrapolates some of FURT's characteristic forms of texture and co-ordination into the octet context of the fORCH ensemble. The results of these more experimental and collaborative projects have exerted an increasing influence on Barrett's other compositional work, which remains mostly fully notated, although several compositions (for example transmission, Blattwerk and adrift) alternate between precise scoring and free improvisation for part or all of their duration. However, these different strategies are used to maximise the musical potential of the whole, rather than drawing attention to the distinction between improvisational and notational methods of composition—as Barrett himself puts it (Barrett 2009): "As a listener I generally prefer to concentrate on what music is doing rather than how it was done".
Since 2003 he has been working on an eight-part cycle of compositions collectively entitled resistance & vision and with a projected total duration of over six hours, of which the first (NO), third (cell), fifth (Mesopotamia), sixth (IF), seventh (Nacht und Träume) and eighth (CONSTRUCTION) have so far been completed (April 2015). CONSTRUCTION is itself a conglomerate work lasting over two hours in performance, consisting of twenty components in four interwoven cycles which may also be performed singly or in various combinations. Since the completion of CONSTRUCTION he has been working concurrently on a number of other projects which continue long-term associations - life-form for cellist Arne Deforce and world-line for ELISION - as well as inaugurating a new one - close-up for the Belgrade-based group Ensemble Studio6.