In 1980, Jacobi took the leading role in the BBC's "Hamlet", made his Broadway debut in "The Suicide" (a run shortened by Jacobi's return home to England due to the death of his mother), and joined the Royal Shakespeare Company (RSC). From 1982 to 1985, he played four demanding roles simultaneously: Benedick in Shakespeare's "Much Ado About Nothing", for which he won a Tony for its Broadway run (1984–1985); Prospero in "The Tempest"; "Peer Gynt"; and "Cyrano de Bergerac" which he brought to the US and played in repertory with "Much Ado About Nothing" on Broadway and in Washington DC (1984–1985). In 1986, he made his West End debut in "Breaking the Code" by Hugh Whitemore, starring in the role of Alan Turing, which was written with Jacobi specifically in mind. The play was taken to Broadway. In 1988, Jacobi alternated in West End the title roles of Shakespeare's "Richard II" and "Richard III" in repertoire.