Cockrill is a second generation Modern British artist of the Liverpool School, whose work defies conventional categorization, and whose teaching career remains impressive. Initially Cockrill employed Pop Art and Photo-Realist styles, very much in keeping with the work of Liverpool's father of Pop-Propaganda, Adrian Henri. During the 1980s, Cockrill moved towards Romantic Expressionism, as shown in his retrospective at the Walker Art Gallery, Liverpool in 1995. A winner of numerous awards throughout his career including the John Moores (1974), Arts Council of Great Britain (1977) and the British Council Award (1985), Cockrill was appointed during 2005-2011 as Keeper of the Royal Academy Schools.

Cockrill's works are in a number of collections including the Arts Council of Great Britain, Welsh Arts Council, Walker Art Gallery, Liverpool, Ulster Museum, Belfast, Kunstmuseum, Dusseldorft and the Centro Cultural Arte Contemporaneo, Polanco, Mexico.