Having served his military service in Vienna, Austria, he studied literature at Worcester College, Oxford.
[1] There, he became acquainted with notable Austrian émigrés such as the composer Egon Wellesz and the musicologist Otto Erich Deutsch.
In 1959 Branscombe joined the University of St Andrews' faculty of German Studies, a post he kept until the end of his life.
In 1979, he founded St Andrews' Institute for Austrian Studies, the only such research facility in the United Kingdom.
Over many years, he wrote reviews of concerts and recordings and contributed to The Grove Dictionary of Music and Musicians and the Wagner-Handbuch (Wagner Handbook) where he researched many forgotten composers of the 19th century.