In 1952 Davis worked at the Royal Festival Hall, and in the late 1950s conducted the BBC Scottish Symphony Orchestra. He started to become well-known when he was suddenly asked to conduct Wolfgang Amadeus Mozart's opera "Don Giovanni" at the Royal Festival Hall because Otto Klemperer was ill. A year later, in 1960, he conducted Mozart's "The Magic Flute" at Glyndebourne because Thomas Beecham was ill.