Jacobi was increasingly busy with stage and screen acting, but his big breakthrough came in 1976 when he played the title role in the BBC's series "I, Claudius". He cemented his reputation with his performance as the stammering, twitching Emperor Claudius, winning much praise. In 1979, thanks to his international popularity, he took "Hamlet" on a theatrical world tour through England, Egypt, Greece, Sweden, Australia, Japan and China, playing Prince Hamlet. He was invited to perform the role at Kronborg Castle, Denmark, known as Elsinore Castle, the setting of the play. In 1978, he appeared in the BBC Television Shakespeare production of "Richard II", with Sir John Gielgud and Dame Wendy Hiller.