Cork was Slade Professor of Fine Art at Cambridge from 1980–90, and the Henry Moore Senior Fellow at the Courtauld Institute of Art in London from 1992–95. He then served as Chair of the Visual Arts Panel at the Arts Council of England until 1998. Committees he has sat on have included that of the Hayward Gallery, the British Council's Visual Art Committee and the Advisory Council for the Paul Mellon Centre for Studies in British Art. He has also been on the panel of judges for the Turner Prize and other major art prizes. In 1995 he was a selector for the British Art Show.