Born in Ayr, Scotland in 1928, Thomson began his studies at the Royal Scottish Academy of Music in Glasgow. In an effort to further his education, he traveled to Germany and Austria; first to the Staatliche Hochschule für Musik in Hamburg, where he studied with Hans Schmidt-Isserstedt beginning in 1954, and later to the Salzburg Mozarteum where he worked with conducting virtuoso Igor Markevitch.
Upon his return to home in 1958, Thomson received his first major appointment with the BBC Scottish Symphony Orchestra, where he served as the assistant conductor to music director Ian Whyte. As fate would have it, Whyte became stricken with a terminal illness and was forced to delegate a number of performances to Thomson, who commanded great praise from musicians, audiences, and critics alike. Within months of these successful concerts, Thomson's guest conducting appearances grew more and more frequent, with orchestras both at home and abroad, including Canada, Scandinavia, and South Africa. He left the Scottish Symphony in 1962, in order to focus on his guest conducting. He was appointed as the associate conductor of the Scottish National Orchestra in 1966.
In 1968, only two years after his first major music director appointment, Thomson became the music director of the BBC Northern Symphony Orchestra in Manchester (since 1982 this orchestra has been known as the BBC Philharmonic). He also assumed the post of music director with the Ulster Orchestra in Belfast, Ireland, which he held until 1985.
From 1970 to 1988, Thomson recorded nearly fifty compact discs for Chandos records, most of which feature composers from the British Isles, although his notable affinity for Nielsen and Martinu spawned several fine recordings of works by these composers. In addition to his set of Bax symphonies, Thomson also recorded the Symphony cycles of Martinu, Elgar and Vaughan Williams, in addition to a number of works by lesser-known composers.
In 1988, Thomson returned to the (now Royal) Scottish National Orchestra, where he was invited to succeed Neeme Järvi as music director. Always active as a commissioner of new works, Thomson commissioned fellow Scottish composer John Maxwell Geddes for his Symphony No. 2. Unfortunately, Thomson died before the work could be completed. Once finished, Geddes added the subtitle 'In memoriam Bryden Thomson'.