See a range of free shows at the Scoop, near Tower Bridge.
Royal Festival Hall
This hulking presence on the South Bank was built for the 1951 Festival of Britain. Sixty years on, it's still at the forefront of London's cultural scene. Although primarily a hall for major concerts, it's a pretty safe bet that the ground-floor stage area will be busy with a free concert, exhibition or workshop, especially if you visit on a weekend. While you're there, be sure to take the singing glass elevator up to the fifth floor, where you'll find a little-known balcony area with impressive views of the Thames. There's free Wi-Fi throughout the building, too.
• Southbank Centre, Belvedere Road, SE1,020-7960 4200, southbankcentre.co.uk
The famous courtyard and vast Georgian building alone are worthy of a visit, but seek out the two elegant staircases, the balcony views of the Thames, and the small basement gallery. In the summer, the dancing courtyard fountains are a joy. In the winter, an ice rink takes over. Occasionally, the house's catacombs are opened for art installations and performance. The house also contains the Cortauld Gallery of impressionist paintings, though an entrance fee applies here.
• The Strand, WC2, 020-7845 4600, somersethouse.org.uk. Open Mon-Sun 10am-6pm
The British Film Institute's swanky South Bank complex has much to explore, including two excellent bars, cinema screens, a well-stocked film store and a small exhibition space. Its greatest treasure, however, is the Mediatheque. This suite of wide-screen computer booths offers free access to thousands of archive TV shows, films and documentaries, including plenty of material about London itself. Book ahead or simply turn up at a quiet moment.
• Belvedere Road, London, 020 7928 3535, SE1, whatson.bfi.org.uk/Online/default.asp. Open Tue-Fri 12 noon-8pm, Sat-Sun 12.30pm-8pm
Just north of the exhausting crowds of Oxford Street stands Hertford House, home to the Wallace Collection. The sizeable galleries are noted for the fine paintings, displays of weapons and armour, and elegantly furnished rooms. Painters represented include Rembrandt, Titian and Van Dyck, and the Wallace is also home to the famous Laughing Cavalier by Frans Hals. The restaurant in the central atrium must rank among London's most exquisite gallery dining spaces.
• Hertford House, Manchester Square, W1, 020-7563 9500, wallacecollection.org. Open Mon-Sun 10am-5pm
Photograph: Linda Nylind/Guardian
The South Bank isn't entirely given over to professional concerts and high-brow culture. A popular skate park lurks beneath the Queen Elizabeth Hall, with enough ramps and raised surfaces to keep a couple of dozen skateboarders and BMX riders happy. It's also a popular spot for graffiti artists who can hone their skills without being collared. Even if you're not a skater, the spectacle is worth a diversion. Nearby, on the north-east pontoon of Hungerford foot bridge, is a "skateboard graveyard", into which broken decks are pitched.
• Southbank Centre, Belvedere Road, SE1, 020-7960 4200, southbankcentre.co.uk
Although many of London's museums and galleries are free, it's a little harder to find theatre or cinema that doesn't come with a ticket price. One hotspot for gratis performance is The Scoop. This sunken space seats 800 and can be found beside City Hall, close to Tower Bridge. During summer months, the amphitheatre is in use almost every evening, hosting live music, plays, film screenings and keep-fit classes. While you're in the area, take a look inside City Hall where a spiral ramp leads down to small gallery spaces, a cafe and a giant map of London. The security can look a bit fearsome, with airport-style scans – but don't worry, you have every right to go in.
• City Hall, 110 The Queen's Walk, SE1, 020-7403 4866, morelondon.com/scoop.html