Born in Birmingham, Abbott studied music at Birmingham and Reading Universities before attending the Royal College of Music to study with Gordon Jacob (orchestration), Richard Austin (conducting) and Frank Probyn (horn). He conducted many operetta and musical productions in London and on tour and composed much incidental music for the theatre.
He joined the Royal Ballet as a conductor for the tour of Australia and New Zealand in 1958-9 and then the BBC as Music Producer (Radio), working mainly with the BBC Concert Orchestra. In 1965, he left to take up the position of Musical Director at Turkish State Ballet and in 1971, he became Resident Conductor of Australian Ballet, where he remained for five years, before moving on to become Musical Director of Western Australian Opera and the Western Australian Arts Orchestra. He returned to Britain in 1979 and became a guest conductor for Paris Opera Ballet, the Royal Swedish Ballet and Norwegian National Ballet.
Abbott is well known as an editor and orchestrator of music, mainly for television and recordings.