Herron and Chalk were founding members of Archigram (1960). Located directly next to Lasduns National Theater begun in 1967 the gallery is part of the Southbank Centre on the southern bank of the Thames. It houses both the collection but also the temporary exhibitions of the Arts Council of Great Britain (today Arts Council of England), which concentrate on modern and contemporary art. Perched on a high base the building sets itself apart from street level and attempts to separate pedestrians from cars. The characteristic roof structure with pyramid-shaped additions makes for even light in the exhibition rooms.

The Hayward Gallery was renovated from 2015 to 2018 according to plans by Feilden Clegg Bradley. Among other things, the approximately 60 steel and glass pyramids on the roof of the gallery were repaired, and a false ceiling that obstructed the natural light entering the upper galleries was removed.

The building is not currently listed. Although the Hayward Gallery is considered a significant example of Brutalist architecture, it has been refused listed building status on several occasions. Applications for inclusion on the list of listed buildings were rejected in 1992, 1998, 2006 and 2010. In 2011, the Hayward Gallery was added to the list of protected buildings by the World Monuments Fund, but this does not confer legal listed building status in the UK. 

In February 2020, the Culture Secretary Baroness Morgan of Cotes granted a Certificate of Immunity from Listing for the Queen Elizabeth Hall, the Purcell Room and the Hayward Gallery. This certificate prevents these buildings from being listed for a period of five years (last updated on January 6, 2025).