Let's face it, London is famous for a lot of great things – the eponymous Great Fire for instance, and being the biggest city in Great Britain, too. But one great thing it's not well known for is the great outdoors – which probably has something to with the fact that it's difficult for you to get much of a sense of escapism or freedom while you're still inside the South Circular.

City dwellers, fear not: although the naysayers would have you think lofty sports like ice climbing and wild camping were made for the wilderness regions of the US, Canada and Scandinavia, you can actually get to grips with them pretty easily without straying too far from London – you just need to know where to look.

Luckily, we've done the searching for you, so here are some of the greatest ways to do extreme things in unexpected places, from underground potholing in East Ham to wall climbing in Bermondsey, and wild camping and bushcraft classes out on the on the city's fringes.

1. Bushcraft in Broxbourne

With weekend crash courses in bushcraft and fire-cooking from spring, at Lee Valley's Almost Wild campsite, you can pretend you're in the taiga forests of Sweden instead of a few miles north of Tottenham. Camping £12pp per night; bushcraft classes £10 per session. visitleevalley.org.uk

Nearest London Tube station: Broxbourne (National Rail)

Ice Climbing at Vertical Chill in Covent Garden, London

Vertical Chill brings ice climbing to central London

2. Ice climbing in Covent Garden

There's something awfully pleasurable about sinking a pointed piece of metal into a slab of ice and hauling yourself up agonisingly limb by limb. Give it a go at Vertical Chill's 8m ice wall, which you'll find at the back of Ellis Brigham near Covent Garden. One-hour session, £50. vertical-chill.com; ellis-brigham.com

Nearest London Tube station: Covent Garden

3. Wild food walks across the city

Know your hogweed from your hemlock and your chanterelles from your – well – downright deadly mushrooms? Good. But Forage London probably knows them better. Join them for a weekend foraging walk and you might just be able to use London as your larder. Day walks from £35. foragelondon.co.uk

4. Indoor Caving in East Ham

You know how the old adage goes: 'You don't know a city until you've seen its sewers'. Sure, this all-new subterranean experience at Flip Out in East Ham doesn't take you to the actual abyss under the city, but its 100-yard caving course is about as close as you'll get without initiating your gag reflex. One-hour session £10. flipout.co.uk

Nearest London Tube station: East Ham

5. Bouldering in Bermondsey

No amount of chalk with help you get a grip on the wet outdoor walls of Britain in winter. Fear not: at The Arch, you can climb hundreds of regularly changing routes across its two sites in Bermondsey, then hit the Beer Mile for a celebratory pint or three once you're done. Day entry from £8.50. archclimbingwall.com

Nearest London Tube station: Bermondsey

6. SUP and kayak Central London

If you're yet to paddleboard the cold waters of Kew or head intrepidly out on your own kayak-driven booze cruise between Limehouse and Hackney Wick, it's probably safe to say you're not doing London probably. Thankfully, Secret Adventures is doing something about about that, and can get you doing exactly that. From around £55. secretadventures.org

7. Learn to lead climb in Stoke Newington

Struggling to find sheer, stony slabs anywhere in central London? No problem. At this 160-year-old castle in Stoke Newington there are tons of regularly changing climbing routes built up old turrets and down into underground wells. It's about as close to traditional outdoor climbing as you're ever likely to get without leaving zone 2. One-day intro courses £57; day entry from £12.50. castle-climbing.co.uk

Nearest London Tube station: Manor House