Denny studied in London, initially at St Martin's School of Art from 1951-1954, followed by the Royal College of Art, 1954-1957. He began teaching first at Hammersmith College of Art, 1957-1959 and Bath Academy of Art, 1959-1965, later moving to the Slade School of Art, London where he became Principal Lecturer. He was also Visiting Professor at the Minneapolis Institute of Fine Art.
He exhibited at the Young Contemporaries in 1953 and had his first solo show at Gallery One, London in 1958. However, it was at the British Situation exhibition in 1960 that Denny received real recognition. His work represented Britain at the Venice Biennale in 1966. Denny was one of the first artists in Britain to respond to American Abstract Expressionism.
In order to emphasise the objectivity of his paintings, at one point he exhibited them resting on the floor. He has written on art for international art magazines such as Das Kunstwerk and Art International.
A retrospective exhibition of Denny's work was held at the Tate Gallery, London, 1973. Public collections include; The Arts Council, London, Calouste Gulbenkian Foundation, Lisbon, Museum of Modern Art, New York and the Ulster Museum, Belfast.