Morris featured in over fifty films; a notable early role was as Thorburn, the oddball pornographer running a Soho bookshop in John Gilling’s science fiction thriller The Night Caller (1965). His better known films include Woody Allen's Love and Death (1975), Ken Russell's Lisztomania (1975), and Gene Wilder's The Adventure of Sherlock Holmes' Smarter Brother (1977). He also appeared in many television programmes, his debut being in a BBC production of the comedy Fly Away Peter (1948). Although most of his television appearances were in Britain, such as Z-Cars and Lovejoy, he also made some appearances in US programmes, such as a Columbo movie titled Ashes to Ashes (1998) and the Dennis Miller comedy vehicle Bordello of Blood (1996).