From gay urinals to a Prada store in the Texas desert, the Scandinavian duo are as playful as they are provocative – as their clashes with Boris Johnson over the fourth plinth rocking horse proved

There’s something hanging in the Berlin studio of Michael Elmgreen and Ingar Dragset that is unusual even by their peculiar standards. At first glance, it’s just a punchbag. But, as you approach it, you notice that its blue fabric is decorated with the stars of the European Union. “We’re calling it Anger Management,” chuckles Elmgreen. “We might offer Boris Johnson a 10% discount.”

The punchbag has many of the hallmarks of the artistic duo’s work – it’s instantly humorous, yet probes for a deeper response. Should you punch it, as the object suggests, or embrace it, as your political leanings might prefer? And, if it’s a piece of art, should you even punch it in the first place?

Provoking responses, rather than “making art”, has been Elmgreen & Dragset’s mission ever since they formed an artistic partnership in 1995. Over two decades they’ve repeatedly challenged the hushed and respectful way the public are expected to interact with art. They’ve transformed galleries into nightclubs, drawing rooms and eerie hospital waiting areas. They’ve placed diving boards out of windows, dropped a Prada store into the middle of the Texan desert and gatecrashed a favoured viewing spot of the Statue of Liberty by installing a massive and unusable telescope.

Facebook Twitter Pinterest Down the toilet … Elmgreen & Dragset’s Gay Marriage. Photograph: Matthias Kolb/courtesy of the artist and Whitechapel Gallery

Their work is subversive yet playful. In 2001, when they were asked to show at the Tanya Bonakdar gallery in New York’s Chelsea, they decided to comment on the area’s creeping gentrification. Aware that the downtown Guggenheim had just been redeveloped into a Prada store, they covered the gallery with a facade that read: “Opening soon – Prada!” It worked but not in the way art is “supposed” to work. Clients called to say how sorry they were that they were going out of business. Others inquired as to who would be designing the new store. And pretty much nobody bothered entering the gallery itself.

“Yes, and our relationship [with the gallery] never really recovered after that,” says Dragset, unable to contain his laughter.

Elmgreen & Dragset are rather like their art – mischievous and multi-layered. Dragset has a full-beam smile and a charming giggle, while Elmgreen, the more talkative of the two, likes to slouch back in his chair and, with an air of comedy, offer his disgust at things – authority, labels, critics. (“I hope he’s not slagging off your colleagues,” says Dragset.) They were boyfriends for their first decade together. When they split – an event they describe as “painful” – it wasn’t enough to halt their artistic partnership.

Facebook Twitter Pinterest ‘We will have cocktails in the evening and cry on each other’s shoulders’ … Michael Elmgreen, left, and Ingmar Dragset Photograph: Elmar Vestner

We meet at their studio, a giant, light-filled former water pumping station in Berlin’s Neukölln district. From the ground floor, it seems like a minimalist cathedral, while upstairs are workspaces, a room with a grand piano, and a kitchen. They’re here to talk about their forthcoming show at the Whitechapel gallery, London, entitled This Is How We Bite Our Tongue, their first major overview in the UK. They have rebuilt the gallery’s ground floor level, turning it into a room with a completely different function. It’s another comment on gentrification and will showcase their brilliance at transforming architectural spaces.

Despite their fondness for ambitious projects, neither Elmgreen nor Dragset had any artistic training. They think it’s been a blessing, allowing them to experiment within the relatively small Copenhagen art scene where they met, free from commercial pressures. Elmgreen started his artistic life as a poet, while Dragset came from a theatrical background, but both were hungry for ways to make a greater connection with their audience. Their early days sound like a blast – they would put on performances in public toilets, present operas, or stage 100-day-long happenings in abandoned spaces. “There was no five-year plan: how to become artists,” says Elmgreen. “It just happened.”

The pair liken their partnership to one of their own artworks, Gay Marriage, which presents two urinals, linked as one by an intertwining metal drainage pipe. How did they manage to continue once their romantic relationship ended?

“Oh, that helped the marriage,” says Elmgreen. But it was tough at first. When looking over the chronology for their Whitechapel show they realised that the year they split, 2004, contained just one exhibition and almost no work. They credit Tate Modern’s then curator Susan May with saving their working relationship: “She said, Please don’t cancel your exhibition. We will have cocktails in the evening and cry on each other’s shoulders.’ And that’s what we did.”

Facebook Twitter Pinterest Howls of protest … the stainless steel sculpture HAN, in Elsinore, Denmark. Photograph: Anders Sune Berg

“It wasn’t easy,” says Elmgreen, “but easy is not always the right solution. In the end, it was good not to be this ingrown married couple that would do everything together and just experience the same things. We would come in with different input, like in the beginning. We had to respect each other in a different way.”

Looking at things in a new light is key to much of Elmgreen & Dragset’s work. Their series of self-portraits, also on display as part of the Whitechapel show, present not their faces but their artistic inspirations, portrayed as exhibition information labels, rendered in oil paint or marble. They are, says Elmgreen, a reaction to “banal” selfie culture. “There are so many more complex ways of constituting one’s identity,” he says. “It’s dangerous to perceive the world only through showing your happy face in front of some landmark or disaster.”

For artists so keen on public interaction, the pair largely disregard social media. They rarely post on Instagram, and don’t consider it while making new works, except that they now use more durable materials – the curse of public art in the selfie era is that people have a habit of stepping on the work while they’re posing.

Still, their favourite readings of their work often appear online. After they put The Experiment on display at the Met in New York – a sculpture of a small boy wearing underpants and his mother’s high-heeled shoes, examining his reflection in the mirror – people took to social media to share their own gender experiments. When they transformed part of the National Gallery in Copenhagen into a hospital ward with four beds, a work that was intended to be a comment on institutional conventions became a therapeutic experience for many who walked through it. “People talked about their own history of illness, or loss in their family,” says Dragset. “It wasn’t what we expected.”

Facebook Twitter Pinterest ‘Don’t call it an anti-war memorial,’ said Boris Johnson … Powerless Structures, Fig 101 on the fourth plinth in Trafalgar Square in London. Photograph: James O Jenkins

They find such readings more interesting than the opinions of most critics who, they say, often lazily repeat whatever’s been said about them in the past. They hate being called ironic, or sarcastic, or pranksters, or protest artists: “It seems a bit like we hate everything,” grins Dragset. The humour, says Elmgreen, is a device to express things they find depressing or difficult to handle. They insist that any provocation is never intended. “It creates attention, but the conversation becomes very basic.”

When they were commissioned to make a sculpture of a male mermaid for Elsinore in Denmark, they were met by unexpected howls of protest that the proposed figure was too effeminate and an insult to the metal workers who used the site, a former shipyard. “We got the most incredible letters to the local newspapers,” says Dragset, “saying, ‘First we had the Swedes coming over drunk, and now we’re being invaded by gay people!’”

In 2011, when they were awarded a spot on the fourth plinth in Trafalgar Square in London, and displayed their sculpture of a young boy on a rocking horse, they were warned by Boris Johnson not to label it an “anti-war memorial”. “And you’re just looking at him and thinking, ‘How naive can you be?’,” says Elmgreen, eyes widening. “‘When you’re out of the door we do exactly what we want!’”

Johnson proved to be an irritant throughout the project. For one press conference, Elmgreen says he turned up late and totally unprepared before telling the assembled journalists that the boy represented Britain’s gold medal hopes in the Olympics. “I had to take the microphone in a very soft way and say, ‘I think I’m going to help you out here because that’s not what it’s about.’”

Admiral Nelson is a little camp, too, when you see him close up

What Powerless Structures, Fig 101 was actually about was masculinity and innocence, an antidote to Trafalgar Square’s assembled war heroes whom they dismiss as “grumpy old men in black robes”. Their boy, in his skimpy lederhosen, was deliberately camp – the kind of subtle message the likes of Johnson were so afraid of letting slip through the net.

“Although Nelson is a little camp, too, when you see him close up,” says Dragset. Is he really?

The pair look at me as if I might be blind for not noticing. “He’s standing like this on his column,” says Elmgreen, leaping up and putting his hand on his hip as they both start cracking up.

It’s tempting to think that being in Elmgreen & Dragset must be a hoot. But it’s clear that the pair take art, and its power to change the way we view the world, extremely seriously. Their aim isn’t to provide a laugh, but to help people question the norms and power structures of society.

“In these times when there’s so much populist politics all around us, art needs to do a better job of not being in an ivory tower,” says Elmgreen. “Not being too hermetic. Not being behind closed doors.”

Most of what they do – perfecting the idea, sourcing quality materials, ensuring the concept works within the space – is, they say, a real headache. A hard slog. But, as Elmgreen concludes, with the same deadpan air as much of their work, “there’s at least 2.5% fun”.

• Elmgreen & Dragset: This Is How We Bite Our Tongue is at the Whitechapel Gallery, London, from 27 September to 13 January.