Robert Demeger trained at the Central School of Speech and Drama. In theatre he appeared in several roles for the Kick Theatre under Warner, including King Lear in the 1985 adaptation at the Almeida Theatre and later in Jew of Malta at the same venue, as well as several roles in productions with the Royal Shakespeare Theatre. He also appeared three times in The Woman in Black, and played Neville Chamberlain in Three Days in May.

In television he had roles in a number of crime dramas, including Inspector Morse, Wycliffe, The Bill and even The Thin Blue Line. Other roles included Einstein in Dark Matters, Malcolm Lyon in The Hour, and his appearance in Doctor Who as The Preacher in The Shakespeare Code.
Films he appeared in included Wuthering Heights, Orlando and The Young Poisoner's Handbook.

Diagnosed with brain cancer, Demeger undertook a revolutionary form of immune therapy from the United States, becoming the first European patient to do so; however, treatment was found not to work in his case.