The ICA was established in 1946 by Roland Penrose, Herbert Read, and a group of artists, writers, and critics who had grown frustrated with the conservatism of the Royal Academy. Their explicit model was the Leeds Arts Club of 1903 — a multi-disciplinary space for avant-garde debate with a radical social outlook. The first exhibitions were held in the basement of the Academy Cinema on Oxford Street; the title of the second show, '40,000 Years of Modern Art,' reflected the founders' determination to set contemporary work in the broadest possible context. By 1950, the ICA had acquired premises at 17 Dover Street in Piccadilly — formerly the home of Vice Admiral Horatio Nelson — where the bar was decorated by Eduardo Paolozzi and a metal and concrete table was designed by Paolozzi and his student Terence Conran. In 1968, with support from the Arts Council, the ICA moved to its current home at Nash House on The Mall, where it has remained.

The list of what first happened at the ICA reads like a counter-history of British culture. The Independent Group — artists and critics who gathered there between 1952 and 1963 — effectively launched British Pop Art. Richard Hamilton curated 'Man, Machine and Motion' in 1955; his later collage 'Just what is it that makes today's homes so different, so appealing?' is often cited as the first work of Pop Art. In 1968, Jasia Reichardt curated 'Cybernetic Serendipity,' one of the first exhibitions anywhere to present computer-generated art. Adam and the Ants played their official debut concert in the ICA restaurant in 1977 — a performance that was shut down after one song and resumed later that day. Damien Hirst's first solo show in a public gallery, 'International Affairs,' was held here in 1991. The world's first cybercafe operated in the ICA theatre in 1994. Through these decades, the institution also hosted Václav Havel, Patti Smith, Pierre Schaeffer performing Musique Concrète, and the first UK screening of Guy Debord's deliberately unwatchable film.

The ICA's history is not one of smooth institutional progress. For a period in the 1990s, the electrical goods company Toshiba paid to have its logo on every piece of ICA publicity, effectively renaming the institution 'ICA/Toshiba.' A financial crisis in the late 2000s, following the directorship of Ekow Eshun, brought the organization to the edge of closure — redundancies, resignations, and warnings that the building might need to be vacated. The ICA survived, as it has survived repeated predictions of irrelevance. Stefan Kalmár's directorship from 2016 to 2021 brought renewed international focus, though he cited concerns about Right-Wing attacks on arts funding post-Brexit when he departed. The Covid-19 pandemic closed the building from March 2020; it reopened in July 2021 with an exhibition focused on state violence and institutional racism targeting Britain's Black communities. More recently, a 2024 renovation by Sanchez Benton Architects uncovered windows to admit more natural light and replaced harsh fluorescent lights to reduce sensory stress for neurodivergent visitors.

Nash House sits inside Carlton House Terrace, a stucco-fronted Regency block designed by John Nash, steps from The Mall, within sight of Buckingham Palace, and next to the Duke of York Steps. The setting is magnificent and improbable — one of London's grandest addresses housing an institution whose mandate has always been to challenge and provoke. The building contains galleries, a theatre, two cinemas, a bookshop and a bar, all compressed into a narrow terrace house that has been expanded and adapted without ever quite resolving the spatial puzzle it presents. Walking through its galleries today, you are following paths taken by Man Ray giving a lecture on painting, by Francis Bacon being publicly discussed, by Victoria Wood performing on the same evening as Adam Ant's ill-fated debut. The ICA has managed, repeatedly, to be the place where British culture went first.