Artist Damien Hirst's retrospective contributed to a 9% rise in Tate Modern visitors, which had 5.3 million.
Despite bad weather and the Olympics, there was an overall 5.1% increase in visitors at all UK attractions, from 87.7 million in 2011 to 92.1 million.
Visitors were briefly deterred from central London during the games, but Alva director Bernard Donohue called the recovery "almost immediate".