In New York City from 1960 to 1963, he had a relationship with Barbra Streisand, including living together for a year, during which time he helped her develop the nightclub act that began her successful career as a singer and actress.
He moved to London for fifteen years and in 1968 landed the starring role of the master of ceremonies in the London version of Cabaret. In 1970, he played Pontius Pilate on the album of Jesus Christ Superstar, and he played the same role in the Broadway production (1971). In the same year, he played Mendel in Norman Jewison's film of Fiddler on the Roof. According to Dennen's website, he suggested to Jewison that he direct a film of Superstar. Jewison did so, and Dennen played Pilate again (1973).
Since that time, Dennen had a variety of small parts on American television shows and films, including: Superman 3; The Kentucky Fried Movie; The Shining; Galtar and the Golden Lance; Tales from the Darkside and Titanic. He played auto dealer Irwin Lapsey in Shock Treatment, the sequel to The Rocky Horror Picture Show. He also provided his voice for many video games.
He died due to complications posed from an earlier head injury, with his being the second Metal Gear Solid 2 English actor to die in 2017, the other being John Cygan on May of that year.