From 1953 to 1958, he studied architecture at Bournemouth College of Art, and then moved to the Architectural Association School of Architecture in London, graduating in 1960. He later returned to the AA as a teacher.
While working in the office of James Cubitt & Partners, Cook was one of the founding members of the influential Archigram group in the 1960s. In 1969 he received a grant from the Graham Foundation for work done with Archigram.
He was Director of the Institute of Contemporary Arts in London, from 1970 to 1972.
In 2002, Royal Institute of British Architects awarded Archigram the Royal Gold Medalfor architecture. In 2004, he was shortlisted for the Stirling Prize with Colin Fournier for the Kunsthaus Graz. In 2007, he was made a Knight Bachelor in the Queen’s birthday honours.
– Trondheim Library, with Christine Hawley, 1977
– Housing at Lutzowplatz, Berlin, 1989
– Canteen Block HbK, Frankfurt, 1989-92
– Pavilion for the Botanical Garden, Osaka, Japan 1990
– Museum of Antiquities in Bad Deutsches Altenberg, Austria,with Christine Hawley, 1995
– 2012 London Olympic Stadium