Hanging by his fingertips, a man in a paisley headband hoists his heel onto the angular ledge above him. With a muscle-popping moan he leaps for the next 'rock', a blue lump that looks like Play-Doh, and catches it, leaving a cloud of chalk dust in the air behind him as his legs swing wildly from his hold.

A group of casually dressed, toned onlookers stare upwards at him. They rub their powdery white hands together and nod with approval as he completes his dramatic ascent.

This is the world of indoor climbing. A multicoloured playground for adults, complete with blaring drum and bass, dazzle paint, and bright red crash mats. As the clock strikes 6pm at the Biscuit Factory, the Arch Climbing Wall's new bouldering-only centre in Bermondsey, a steady flow of office workers make their way through the door to get their fix of this addictive sport.

Statistics released last week by Sport England reveal that indoor climbing will overtake its traditional outdoor counterpart as the country's most popular mountaineering activity in six to 12 months. The sport as a whole has been on an upwards trend since 2005 – last year mountaineering was one of only four sports to show an increase in participation. Next year the IOC will decide whether 'sports climbing' will enter the Olympics in 2020. The Olympic nod would no doubt cause another surge of interest.

Of the different types of indoor climbing on offer, rope-free bouldering is the category luring in the most new customers. In the past, indoor climbing was primarily used by climbers to practice their technique safely throughout all seasons. They could gain experience of climbing with ropes in order to progress on to outdoor rock faces. However, as fewer climbers are drawn by the allure of clutching tight to a windswept crag, the art of bouldering has become an attractive pursuit in its own right. Requiring no more equipment than a chalk bag, it is as much about balance and gymnastic ability as it is about strength and stamina. Climbers are invited to tackle 'routes' on low walls, denoted by coloured 'holds'. Each route is graded by ability, so you can chart your progression as you clamber your way around artificial features.

"Indoor climbing is the safest way to do what people perceive to be an extreme sport, in a relatively benign environment," explains Rob Adie, the climbing walls officer for the British Mountaineering Council. "It's a bit like watching Formula One on the TV. It has also definitely replaced gym use - it's a social experience, rather than just being stuck on a treadmill."

In the Biscuit Factory's 'cinema room', complete with projector and sofas, Rupa Chawda, 30, who started climbing in January, is taking a break with friends. As if to prove Adie's point, she explains how she used to go to the gym, but found it "a bit lonely".

"Compared to the gym it's less intimidating - this is a social and laid-back sport," she tells me. "I actually find it really Zen."

Katy Briers, 23, who has been climbing on and off for the past year, agrees: "It's a combination of brainwork and a physical workout. It's also really open and lovely. People will come up to you and say: 'I like how you were doing that, but you just need to twist your foot round like this to get all the way up there.'

"It's quite an easy sell for a single girl too - a friend just says: 'Come along and see a lot of sweaty guys with their tops off!'"

But although the Tarzanesque allure of stripping off and swinging from a rock is too much to resist for a large contingent of climbing males, the sport has a strong and growing female participation. "Sometimes you see a girl who's an amazing climber and it's so inspiring," says Briers.

As Adie explains, women often make better climbers: "In a way women take to it more easily, they are more gymnastic and have better natural balance – men tend to muscle through with the strength that they have.

"If you went to a climbing wall 10 or 20 years ago it would be male dominated, but as a sport it's very accessible to everyone."

So accessible, in fact, that you could even find yourself getting tips from a pro. "I had a masterclass with Johnny Dawes," says Jamie MacLellan Clark, 28, a more experienced climber.

"That's the equivalent of a football fan meeting David Beckham - it's that accessible. You can be on the same wall as the pro climbers and they could be helping you."

Jake Cosgrove, 24, who joined the scene last September and is now hooked, also enjoys the support given by other climbers: "If you're working on a tricky route and then you get it someone will always cheer!"

The Biscuit Factory gets up to 20 new climbers through the door each day, but it is just one of the 10-15 new public climbing walls that open in the UK each year.

According to Adie, the country is almost saturated: "Most towns now have two or three decent walls, but we won't hit a limit of new climbers."

This is good news for Boulder Central, another new bouldering-only facility. The venue opened its doors to climbers in the West Midlands in May.

"We chose our location by picking the spot with the highest population to climbing wall ratio," says Jon Chittenden, the director, who is confident that their business will continue to grow.

"In the past five years there's been a massive boom in bouldering-only centres - many climbing wall owners are finding there are a lot of indoor climbers now who will never go outdoor climbing."

Chris Parker, the project manager for Rockworks, a climbing wall construction company based in Durham, says private walls are also adding to the growth of the sport: "A lot of leisure centres are putting them into squash courts. The demise of squash seems to be the rise of climbing … Also, a lot of schools have them retrofitted into gyms."

Ponteland High School in Northumberland is one such school. Students returned after their Easter holidays to find a 21-metre-long bouldering facility had been erected in their sports hall.

"It fit nicely and was affordable," says Gordon Grier, a PE teacher at the school, who first started climbing aged 13. "We've had a great success with the students already and it's helping us diversify our reach - a different catchment of kids come to climb that wouldn't use the usual school sports.

"It involves a lot of self-reliance. Students with less confidence in team sports can achieve at their own level. They can pick it up and enjoy it very quickly."

As closing time approaches at the Biscuit Factory, the easygoing mix of first-time climbers and pros are winding down. Padding about in their bare feet, stretching off in groups, or sitting back with a coffee, the scene resembles a dance studio crossed with a skate park. This hybrid nature of the sport is evidently a factor in its broad appeal.

But there is also a primal element to climbing which seems to really grab the imagination. When you are on the wall and the adrenaline starts pumping, you are whoever you want to be: an acrobat, an overgrown ape, or even - for the real fantasists - Sylvester Stallone in Cliffhanger. It's just nice to know that you're never more than a few feet from the ground.