It’s a Saturday morning in Southampton, and I am four metres from the ground, clinging to a wall and suddenly remembering that I am terrified of heights. Everything was fine while I was moving, but now I have climbed as high as I can and I can’t find a foothold to start back down. My heart is hammering and my whole body is cold. I could just let go and fall to the heavily padded floor; but although that wouldn’t hurt, it’s somehow unthinkable.

“How did I get here?” I bleat to myself, followed by: “And how do I get down?”

The first question is easy enough. I am here to find out why so many of us are falling in love with indoor climbing. According to the Association of British Climbing Walls (ABC), there were a million visits to indoor walls in 2017, about 100,000 of us climb regularly, and the numbers are growing by 15-20% a year. The sport will get another boost in 2020, when it makes its debut at the Olympics. In 2015, pushing for it to be included, the International Federation of Sport Climbing estimated there were 35 million climbers worldwide.

I’ve tried it once before – two decades ago, in a cavernous former pumping station in north London, but then climbing was a fringe activity, and venues were few and far between. Little had changed since the 1960s, when the first walls were created so that outdoor climbers could get some practice when weather or lack of time kept them from their usual haunts. Numbers have exploded since then. From Stirling to Surbiton, Liverpool to Lyme Regis, there are now 500 or so walls in Britain where the public can “pull plastic”, as it is sometimes known.

Enthusiasts with big homes and deep wallets are even installing their own private walls. David Davis, the former Brexit secretary, put one in the barn of his Yorkshire home and said he used it to teach his children “fear management”.

But Southampton’s Boulder Shack is a converted warehouse, not a politician’s outbuilding, and it’s all about fun rather than fear. When I visit, the centre is hosting “goat yoga”, which turns out to do just what it says on the tin. While a couple of dozen men and women do the downward dog or child pose, pygmy goats share their room, occasionally leaping on to a back for a better view. The organisers describe this as “an amazing way to unwind”, which is surely only true if you’re one of the goats.

Keegan Wilson, 44, who has volunteered to show me around, works for Ordnance Survey. He has been climbing on and off since his 20s, when he was initiated by a brother who ran a climbing centre. He is more of a regular now that back trouble has forced him to give up his beloved football.

Like most indoor climbers, he focuses on “bouldering” – tackling walls of no more than five metres, with no special safety equipment – rather than roped climbing, where lines let you go higher, but with considerably more faff. If that sounds like a soft option, it’s not: the hand- and footholds for bouldering can be little more than bumps in the wall, and that wall sometimes tilts back on itself so that it overhangs the floor. Sometimes it’s essentially a roof, and only Spider-Man would feel at home.

What’s the attraction? “You have to be really focused, present, in the moment,” says Will Leigh, a 40-year-old confectionery developer who has been climbing for a couple of years. “That sounds a bit wanky, but what I mean is, you’ve got to focus on not falling off, there and then. I find it really hard not to think about work and life and all those things. The wall is the one place where you don’t even have to try to switch off. You’re just there.”

“Bouldering gives you an excellent workout without you really knowing it,” agrees Wilson. “For me, at least, this is because your mind is focused on the challenge of the climb. There’s a lot of problem-solving, a lot of working out where to put your hands and feet. And you want to avoid falling! The mental side distracts you from how much all the different muscle groups are working. It is only when you stop that you realise how much you have exerted yourself.”

Climbers talk a lot about “problems”, their term for the often tricky routes that they try to follow up, and sometimes along, walls, using holds of just one colour – sticking faithfully to greens, say, and not so much as touching the blacks, reds, blues, oranges and pinks. Possible solutions are known as “beta”.

“It’s not just about working your body, though that’s where the most obvious benefits are,” says Tiffany Soi, 32, an impressively toned competitive climber who also runs specialised yoga classes. “For a lot of people, it’s very much a therapy.”

Reassuringly, she says, “You don’t need to be a great athlete to get started. All sorts of body shapes, types and heights find that they quickly make progress. That’s quite a positive feedback response, and it’s encouraging and addictive. When people tell me they’re scared that they won’t have the muscles, I say: ‘Just trust me. Come and try because you will be surprised.’”

That was Leigh’s experience. “I’ve never been a really sporty person,” he says. “I was too busy behind the bike sheds when everyone else was playing football. But about two years ago I went bouldering with some friends and I was hooked straight away. You make really quick progress, and within a few months you can be climbing things that you didn’t think you’d ever be able to climb. That, for me, was a real pull.”

Like a lot of climbers, he now feels compelled to spread the word. “I’ve probably become a bit of a bore who runs round telling people that they must try climbing,” he says.

What else lies behind the boom? “People are looking for more than fitness,” says Natalie Berry, 26, a competitive climber and editor-in-chief of UKClimbing.com. “They’re looking for people to hang out with, and in the same way that there’s a social aspect to CrossFit and parkour, this is something you can do with a group of friends.”

“It’s an environment that’s very welcoming,” agrees Leigh. “There is some competition, like at all sporting places, but if you’re struggling you can ask for help. If you want to be on your own, you can stick your headphones on and nobody will talk to you – or you can have a conversation with the person next to you.”

And then you’ll probably go for a coffee together. In Southampton, there are excellent lattes, falafel and mango chutney toasties and raspberry and lemon cake. “A lot of the new walls have discovered that a good cafe can bring people to the facility,” says Berry.

It helps that climbing is fairly cheap: you’ll typically pay £8-11 to use a wall on a one-off basis, and you don’t need to buy or hire much equipment. For bouldering, you’ll get by with a pair of painfully tight shoes and a bag of powdered chalk to improve your grip. For roped climbing, you might want your own harness, but little else unless you are venturing outside.

A lucky few even find love through the sport. It happened for Soi, who met her husband on the climbing circuit; for Gabrielle Bourret-Sicotte, a 24-year-old postgraduate student who met a boyfriend at the Oxford-Cambridge varsity climbing competition; and for Justyna Sowa, 29, a PR and podcast host, who encountered “the love of my life” at the Arch centre in Bermondsey, London. “We started to chat,” she recalls, “and we exchanged numbers, to ‘make sure we could climb together soon’, in a very cheesy way. And now you can’t separate us. It’s become our date night – Saturday night at the climbing gym – because I don’t see watching a film as something that brings you closer to your partner. It’s just over a year now, and we’ve been on climbing trips to the Peak District and Tunbridge Wells. Our holidays are based on being close to boulders.”

Sowa had a nasty fall three months ago and fractured her elbow. “I was afraid because our relationship was built around climbing: ‘What happens if I can’t climb any more?’” But they’ve got through it, and soon she’ll be back on the wall. In the meantime, they’re training for a marathon together.

Women, in particular, say they find the wall more welcoming than the gym, with its often macho and/or sexist vibe. “For a girl it’s non-pervy, it’s super-friendly, super-chilled,” says Sowa, who started climbing a year and a half ago and relishes the way that flexibility can trump brute force. “You see muscly gym guys coming in and thinking they’re going to crush it, but it doesn’t happen for them.”

“I don’t feel at a disadvantage being a girl in the sport,” agrees Bourret-Sicotte, who has been climbing for two years. “If tall strong guys do the climb with a one-arm pull-up, I can do it by throwing my leg into a split and balancing on a hold. My years of gymnastics and synchronised swimming have really helped my flexibility, and that is so important in climbing. So although I am short and relatively weak compared with others, I’ve got a leg-up in other areas.”

When I eventually unfreeze and make it back down to earth at Boulder Shack, I see a lot of little groups standing in front of problems, nodding their heads and gesturing towards holds. “The climbing community is fantastically open and friendly,” says the ABC’s chair, Rich Emerson, who runs centres in Bristol and Glasgow, and has been climbing for 40-odd years. “That’s one reason it’s growing. You’ll get teenagers climbing next to 20-year-olds climbing next to 40-year-olds climbing next to 60-year-olds, and they all get on, sharing information and looking after each other.”

Gabi Xiberras, 51, an assistant head at a Manchester high school, sees similar benefits for young people. She has been climbing for just two years, but ferrying her 14-year-old son Joe to and from sessions since he was nine. He is now a member of the junior GB Climbing Team. “It is a great sport,” she says. “I wish I’d discovered it years ago. And I am so impressed with how it develops young people, learning to deal with pressure, experiencing success and failure and coping with challenge and disappointment in a friendly and supportive environment. It is a sport that boys and girls can do together and that all can excel at.”

On my own brief foray, I share a wall with two seven-year-olds: Wilson’s daughter Melody and her friend Bastian. Melody has been climbing since the start of this year; Bastian since another friend’s birthday party two years ago. They are both, inevitably, vastly better and more confident than me. “I find Melody’s fearlessness and energy inspiring,” Wilson says. “It pushes me on to want to do more.”

That, for him and so many others, is what it really comes down to. “The competition, like running, is with yourself,” he says. “How much can you climb? Can you do the more difficult routes? Can you defy gravity and haul yourself up the wall one more time?”

That’s all a bit theoretical for Melody. She doesn’t even pause when the Guardian’s photographer asks her why she loves climbing. “It’s just fun.”