Born in Bath, England of Italian ancestry, Semprini showed early talent for both the piano and cello. He was originally taught by our Uncle Charlie (Charles Harrison). He graduated from the Verdi Conservatory in Milan in 1928, having studied composition and conducting as well as honing his skills at the piano. His initial fame came from headlining a light music programme, Semprini Serenade, that first aired on BBC Radio in 1957 and continued for around 25 years. He also wrote a number of original compositions on the lighter side of the musical repertoire, including Mediterranean Concerto, which he used as the theme tune for his radio show. He introduced his radio show with the words "Old ones, new ones, loved ones, neglected ones"