Born in 1919 in London, Farncombe studied at the Royal School of Church Music in Canterbury and the Royal Academy of Music, graduating in 1951. In 1955 he founded the Handel Opera Society, which presented the composer's Italian stage works at the Sadler's Wells Theatre in London. He conducted the first modern-day revivals of several operas, including the now-popular Alcina and Rinaldo, and remained the Society's director until 1985.

Farncombe was also active at such festivals as the summer season at the Drottningholm Court Theater in Sweden and Karlsruhe Handel Festival in Germany. He continued to conduct as late as last year, when he led a semi-staged performance of Handel's serenata Il Parnasso in festa at St. John's, Smith Square in London.