Institute of Contemporary Arts

The ICA screens great, unusual films on its two tiny screens, but also has an exhibition area showing interesting and edgy art. The beautiful sandstone building sits on St James’s Park, near to Buckingham Palace—flick through a copy of something highbrow in the ICA bookshop, pretending to be totally above wanting a glimpse of the royals. It’s worth checking out the membership, even if you’re just visiting London. It’s £10 for the year for senior citizens and those under 26 (£30 for older people), and gets you a £4 discount on film screenings, £3 cinema tickets on Tuesdays, and discounts in the shop and cafe.