His father, Stuart Knussen, was principal double bass of the London Symphony Orchestra, and also participated in a number of premieres of Benjamin Britten's music.

[4] In this work and his Concerto for Orchestra (1968–1970), he had quickly and fluently absorbed the influences of modernist composers Britten and Berg as well as many mid-century (largely American) symphonists, while displaying an unusual flair for pacing and orchestration.

A much-admired orchestral work from 1994 is his Horn Concerto written for Barry Tuckwell, which "combines the colorful sound world of early 20th century music with a contemporary approach to time and melody".

Knussen wrote his Songs for Sue, a setting of four poems for soprano and 15-piece ensemble, as a memorial tribute to his late wife, and the music received its world première in Chicago in 2006.

It's not a huge work – about 13 minutes – but it's a big piece emotionally.From September 2006, Knussen was artist-in-association to the Birmingham Contemporary Music Group, and from 2009 to the BBC Symphony Orchestra.

[10] His recordings as a conductor include works by Modest Mussorgsky, Ruth Crawford Seeger, Elliott Carter, Igor Stravinsky, Hans Werner Henze, Toru Takemitsu, Colin Matthews, Alexander Goehr, Robin Holloway and Poul Ruders.