Arnell was educated at the Royal College of Music and taught at Trinity College of Music and Hofstra University. He also served as music consultant at the London Film School. Arnell's many compositions include works for nearly every medium and in many styles. His most successful works are those with a narrative character. An example of this type of work is his score for Punch and the Child. Arnell excels at characterizations in a Romantic style but continued to experiment with new techniques in his later works.