Leighton was educated at Queen's College, Oxford and in 1951 won the Mendelssohn Scholarship, enabling him to continue his studies in Rome.
He won many distinguished prizes and was appointed as lecturer and Fellow of Worcester College in 1968. In 1970 he was made Reid Professor of Music at Edinburgh University. His compositions consist of vocal, orchestral and chamber, and solo instrumental works. They have a romantic, lyric quality and contain virtuoso solo passages. He employs 12-tone composition in the tradition of Berg, a technique that developed from his earlier use of chromaticism. Much of his work is diatonic, however, and he often draws upon the highly organized works of the Baroque period as a model for his work.