Timothy Baxter studied composition at the Royal Academy of Music in London, with the South African composer Priaulx Rainier and later with Alan Bush and with Anthony Milner at Morley College. Also with Elliott Carter, Stefan Wolpe, Witold Lutoslawski and Aaron Copland at Dartington Summer School of Music. He studied direction with Peter Gellhorn.

A freelance musician for a number of years (eg with The London Philharmonic Choir, Ballet Rambert, London Ballet Company, Martha Graham Dancers), he also worked with Jaqueline du Pré as a pianist.

He was Professor of Composition at the Royal Academy of Music 1965-1990, Head of Degree Courses (Masters) with the University of London, and examiner for The Associated Board of the Royal Schools of Music 1966-2004. Since 1990 he has lived in Denmark working as a composer.

There is a growing interest in his music - educational pieces, choir works and chamber music - and it is played in many countries.