Finnissy created the music department of the London School of Contemporary Dance and has been an associated composer with many British Dance Companies, including London Contemporary Dance Theatre, Ballet Rambert, Strider and Second Stride. He has taught at Dartington Summer School, Winchester College, the junior department of the Royal College of Music, Chelsea College of Art and is guest lecturer at many colleges and universities. He has also been musician in residence to the Victorian College of Arts and to the City of Caulfield in Australia and for the East London Late Starters Orchestra. He continues to teach at the Royal Academy of Music in London and has recently been appointed to the Chair in Composition at the University of Southampton.
He is a prolific composer and his exploration of a wide range of music (especially folk music) is combined with a fascination for mathematical structures. This interplay between ideas, on the one hand symbolizing the innocent, unconditional response to music-making and the other rigorous, intellectual processes, frequently creates an emotional quality in his work that has been described as "a happy melancholia". The shifts in balance between these two aspects has given rise to a variety of works ranging from the "complex" pieces where rhythmically independent melodies are piled on top of each other, fragmented and decorated, to compositions which focus on the quality of a single line given the simplest of accompaniments.
Finnissy has been featured composer at the Bath, Huddersfield and Almeida Festivals and his works are widely performed and broadcast worldwide. In February 1999, a Festival at Harvard University in Boston was devoted to his music and several world premieres are taking place at the 1999 Music Factory Festival in Bergen. As a pianist he is particularly associated with the commissioning and performing of new British work: composers who have written pieces specially for him include Elizabeth Lutyens, Judith Weir, James Dillon, Oliver Knussen, Nigel Osborne, Chris Newman, Howard Skempton and Andrew Toovey.
In 1990 Finnissy was appointed President of the International Society of Contemporary Music. He was re-elected in 1993 and in 1998 was made an honorary member of the ISCM. 1996, his fiftieth birthday year, saw recitals of the complete piano music by Ian Pace, recordings of orchestral and chamber works on NMC and the publication by Ashgate of Uncommon Ground, a detailed book about Finnissy's music.