Leyton as a singer is best known for his hit song "Johnny Remember Me" (written by Geoff Goddard and produced by Joe Meek), which reached number one in the UK Singles Chart in August 1961 despite being banned by the BBC for its death references. His follow-up single, "Wild Wind", reached number two in the charts.

Alongside singing, Leyton's acting career saw him appearing in television and films throughout the 1960s. His films included The Great Escape, Guns at Batasi, Von Ryan's Express and Krakatoa, East of Java. In 2009 he also had a small role in the film Telstar, a biopic based on Joe Meek's life in which Leyton himself was portrayed by Callum Dixon.