“Burnt-out cars, drug dealers and bums – there was nothing else here.” Balder Lehmann, a 25-year-old professional skatepark builder, is standing beneath a bridge in northern Copenhagen. “It wasn’t the nicest part of town,” he says, explaining why locals used to avoid the area.

For Lehmann, though, the location was perfect. Last Christmas, using surplus concrete, wood and reinforced steel bars, he began building a skatepark. Over the course of a few months, he and his friends constructed three adjoining sets of ramps.

With its wooden frames filled with rubble and coated in 15cm of smooth concrete, Lehmann’s skatepark is much like the ones he builds for clients – typically municipalities around Denmark – with one exception: it’s illegal.

Lehmann never sought permission from Københavns Kommune, the council that owns the land he built on. And it may not even matter – thanks to the city’s liberal approach to urban development, and the role of skateboarding.

Dubbed Underbroen (“Under the Bridge”), Lehmann’s construction is a prime example of a DIY skatepark – built quickly, cheaply and illicitly, often in a neglected part of the city such as an abandoned building. Reclaiming the city is a motive, too. DIY skateparks often try to revive long-forgotten urban spaces, thus making them busier, livelier and safer.

DIY skateparks exist in many cities, not just Copenhagen. The cluster of ramps and bowls built in the early 1990s below Portland’s Burnside Bridge is widely considered the first of its kind. Yet no city is as open-minded about their construction as the Danish capital.

Hullet (the Hole) is set to be destroyed to make way for luxury apartments. Photograph: James Clasper

A case in point is Hullet (“The Hole”) – a deep concrete bowl built in Copenhagen five years ago. Its creation is steeped in myth. In 2010, an American construction company called Grindline was hired to build a new concrete skatepark in the city. Legend has it the company’s burly builders passed on their expertise to local skaters, who scoped out a suitable location and started digging. Over the course of a year, they dug down two metres and piled up the displaced earth to make the hole deeper, before constructing a smooth concrete bowl.

Inevitably, their activity attracted the attention of the council who got on the phone to a man named William Frederiksen. As well as managing Copenhagen’s largest indoor skatepark, he works for the council’s culture department as a kind of ambassador for skateboarding. Frederiksen says his colleagues wanted to know why the skaters were digging such a big hole, and feared someone might fall into it.

But when he explained what they were doing, the council changed its tune. “They said, ‘OK, we love it and we want to keep it – but we have to figure out some kind of deal,’” Frederiksen explains. Instead of stopping the diggers, the council insisted they put up a fence.

Even though it isn’t always completely legal, sometimes you have to lead the way as a citizen Simon Strange

According to Frederiksen, the council’s open-mindedness about Hullet – and subsequent DIY skateparks such as Underbroen – reflects its broader vision for Copenhagen and the role that skateboarding can play. “It wants the city to be lively, noisy, agile and progressive – and it’s thinking in a different way about how to use city space,” he says.

One measure of the council’s progressive approach is that it consults skateboarders such as Frederiksen when it redesigns public squares and streets, to make them suitable for skating. Tolerance of DIY skateparks is another reflection of its ethos.

One of the architects of that vision is Simon Strange, a member of the Social Democrats, the left-leaning party that controls the council. Elected to city hall a decade ago, he has pushed for increased support for skateboarding – such as funding CPH Open, an annual street-skating competition. He also applauds the development of DIY skateparks.

“You want to have people being active and engaging with their city,” Strange says. “Even though people are changing public space for their own purposes, they do it with love and positive energy because they want to create something.”

In particular, Strange welcomes their regenerative potential. “Very often they’re in places that nobody cares about, areas without attention, so they’re creating something out of nothing,” he says. “Even though it isn’t always completely legal, sometimes you have to lead the way as a citizen.”

Underbroen (Under the bridge) is in a deserted part of town. Photograph: James Clasper

Balder Lehmann agrees. “We could have asked for permission but the council might have said no,” he says. “Then what would we have done?” Eventually, of course, his skatepark came to the attention of the city’s technical and environmental department – and Anders Melamies, in particular, who leads the division responsible for streets and parks in northern Copenhagen.

Strictly speaking, Melamies says, he should have called in the bulldozers. But last year the technical and environmental department adopted a strategy known as Fælleskab København (Co-creating Copenhagen). Its vision is to develop the capital in collaboration with anyone who uses it – residents and tourists alike – to turn it into a “living city … a city with edge”.

In that light, he says his job is to find a way “to create space for skaters in a way that doesn’t interfere with other citizens’ use of the city”. With Underbroen he decided he had three options: “We could tear it down; we could leave it, close our eyes and hope that nothing happens; or we could get in touch with the people using it, and try to find a lasting solution.”

He chose the third option. “If we can explain our issues and have a dialogue, hopefully we can solve them and legalise what they have built,” he says. “It’s an impressive creation and a lot of time has gone into it. I would hate to tear it down.”

Still, the city’s open-minded approach to DIY skateparks doesn’t guarantee their survival. A skatepark built in an abandoned building on the outskirts of Christiania, the infamous free-town, is on borrowed time. Next year the building will become the new home of famous Danish restaurant Noma.

Hullet’s days appear numbered, too. In April, the city decided to turn the area into a “green residential district”, with 69 family homes scheduled to be built by 2019. No mention was made of Hullet.

Daniel Mathew teaches at the Academy for Untamed Creativity – a school that seeks to motivate teenagers to re-enter formal education. He has helped students build three DIY skateparks and insists on getting prior permission from landowners. He says it’s a shame that Hullet’s builders failed to do so.

“They never started a conversation with the guys who own the land and now it’s going to get torn down,” he says. “In two years, it’s game over. It’s a perfect skatepark and it could have been there for 10, 15 years. But that’s the DIY way – it comes and it goes.”

Lehmann stopped building Underbroen in the summer. Having spent 50,000 DKK (£5,660) on it, he’s hoping to get retrospective permission – but is prepared to remove it if he doesn’t.

“That’s the gamble. If it gets torn down, that’s how it is,” he says. “But if it does, believe me, something else is going to get built – because there are a lot of people who want to build their own thing.”

Follow Guardian Cities on Twitter and Facebook and join the discussion