Arnell composed in all the established genres for the concert stage, and his list of works includes six completed symphonies (a seventh was realised by Martin Yates) and six string quartets.
During his American sojourn, Arnell was the Music Supervisor for the BBC in North America, and was commissioned to compose (to a text by Stephen Spender) a cantata, The War God, in celebration of the opening of the United Nations, as well as a fanfare to greet Winston Churchill's arrival in New York.
His music has been championed by Thomas Beecham, Leopold Stokowski and Bernard Herrmann, among others and more recently by Warren Cohen and Martin Yates (one of his composition students at Trinity).
[4] With the exception of a break from 1967 to 1970 to act as Visiting Fulbright Professor at Bowdoin College, Maine, from 1967 to 1968 (in an exchange with Elliott Schwartz), and at Hofstra University, New York, from 1968 to 1970, he taught at Trinity College of Music in London between 1947 and 1987, where his students included Peter Tahourdin (1949–52),[5] electronic composer David Hewson, who worked with him on films including Dilemma (1981), Doctor in the Sky (1984), Toulouse-Lautrec (1986), and The Light of the World (1989), was one of his pupils.
All seven of Arnell's numbered symphonies together with the Sinfonia Quasi Variazioni, the Piano Concerto (soloist David Owen Norris), the two Violin Concertos (soloist Lorraine MacAslan), Lord Byron: a Symphonic Portrait, Robert Flaherty Impression, Prelude The Black Mountain and the early Overture The New Age, received their world premiere recordings by conductor Martin Yates and the Royal Scottish National Orchestra between 2005 and 2008.