Cork's broadcasting work includes reviews of art exhibitions for BBC Radio 4's "Front Row", "Night Waves" on Radio 3 and "The Green Room" on Radio 2. He also regularly appears on the BBC Two art series "The Private Life of a Masterpiece". He has curated exhibitions at the Royal Academy, Tate, Serpentine Gallery, and Hayward galleries in London and, elsewhere in Europe, in Paris, Brussels and Berlin. In Cork's 1978 exhibition, "Art for Whom" at the Serpentine Gallery, "all the work exhibited the idea of community and group experience-a principal of social integration..." (Gablik 12). Cork has a specialist interest in the Vorticist movement and his book on them was for some time the standard text on the movement. In 1995 Cork was given a National Art Collections Fund Award for his international exhibition "Art and the First World War", held in London and Berlin. He is currently a Syndic of the Fitzwilliam Museum, Cambridge.