He studied with Walter Grünner at the Guildhall School of Music and Drama and established an international reputation as a singer when he won a third prize at the 1961 ARD International Music Competition in Munich. Soon afterward he joined composer Benjamin Britten's English Opera Group and on their tour of the Soviet Union in 1963 sang the roles of Sid and Tarquinius in, respectively, Britten's operas Albert Herring and The Rape of Lucretia. In 1971, Britten composed the title role of his television opera Owen Wingrave specifically for Luxon's voice; Luxon created the role later that year with the English Opera Group.