Seven men are struggling with a palm tree. They have pulleys, cables and levers but the weight of the soil and the palm tree’s leaves mean that manoeuvring it into a horizontal position is a complicated business. Horizontal? Yes, because they are installing Henrik Håkansson’s Fallen Forest. A 4m section of tropical woodland is flipped on its side, its trees growing parallel to the Barbican Art Gallery’s planking, while the forest floor points up to the skylights .

Håkansson’s piece is one of the most striking sights in Barbican’s Radical Nature exhibition and visitors can crane their necks to view it from Friday. But what is the point of dragging a chunk of one of the world’s most threatened ecosystems up four flights of steep stairs to the austere white gallery at the City of London’s brutal concrete heart?

Francesco Manacorda, the curator of Radical Nature, is clear. “Fragmentation of habitats in the rainforest is a serious problem but environmental activism on the subject can sometimes be so forceful that it puts people off. Håkansson tackles the question from another direction. Art can pose questions about environmental issues and not force the answer on to people. It’s a different way of doing things.”

Manacorda is tackling the question of our relationship with our planet. The playfulness is still there: the exhibition also features flying gardens, a Buckminster Fuller dome, a miniature grassy knoll and even a small allotment growing under the stairs.

The show aims to convert the whole gallery floor into a single continuous greenscape. Walking in from the Tube station, the visitor’s view of the Barbican centre’s brutal concrete is tempered by the glassy rooftop rainforest that rises above it, a true fantasy conservatory, built in 1980. But can an art exhibition shift thinking about environmental issues? The optimistic catalogue foreword by Jonathon Porritt, former director of Friends of the Earth, shows that he thinks so.

Whether or not you agree with the curatorial line, the show provides the chance to see some stunning exhibits. Out in the desert, a man in white shirt and jeans stands on the rocks at the edge of a body of water. The camera views him from a helicopter and, as it pulls back, we begin to see that he is standing in the centre of a huge curled manmade causeway, stretching out into a dazzling salt lake. “Mud, salt crystals, rocks, water,” is the laconic voiceover, above the noise of the helicopter. This is Spiral Jetty, the vast Utah earthwork made by Robert Smithson in 1970; his film showing off the work is a central piece in the show and this is a rare chance to see it in full.

Another installation by Lothar Baumgarten has a transfixing beauty. Living in Germany in the late Sixties, Baumgarten began working in the polluted industrial zone around the Rhine. Walking, making objects he found into small temporary sculptures, and taking pictures — his slide images from the time have the golden sheen of Seventies Kodachrome, transforming oily swamps into tropical visions.

In that rich light an abandoned piece of tubing becomes a giant jungle centipede. To increase the oddness of the effect, the slideshow plays to a soundtrack of birdsong and animal noise . Baumgarten called the work ELDORADO, adding in brackets: “I Prefer it There Better Than in Westphalia.” The effect is seductive and glossy as well as poignant and meditative.

A big worry about the Barbican staging such an ambitious show is that it is a relatively small space and quickly feels crowded. But this is part of the point: “We want to crowd it, to create a continuous landscape through the gallery,” declares Manacorda. And the works in the Barbican gallery are just the focus for associated projects running alongside the exhibition. By the Barbican’s lakeside is a wooden pavilion by the artists Heather and Ivan Morison, with huge roof tiles like a Russian dacha. Inside it will be a tea pavilion with views out on to the lakeside gardens.

A few miles directly north, in Hackney, the architecture collective EXYZT has created The Dalston Mill, a windmill that will generate electricity and grind flour for bread from July 15. Around the corner from Dalston Kingsland overground station, it will also feature a re-creation of Agnes Denes’s famous 1980s Battery Park installation of a wheatfield, this time growing by an abandoned railway line.

And there are plenty of microevents: for just two days the Wayward Plants Registry will move into a room within the Barbican exhibition space, hosting a plant adoption scheme. Visitors must fill in forms describing what kind of home they could give a plant.

Elsewhere, the neuroscientist and artist Beau Lotto brings his Lottolab to the RSA, exploring the way that the human brain interprets the natural world. He will be talk about his “bee towers” (glass cubes filled with bees and artificial flowers used to study their flight patterns) and will argue that understanding how different individual perception is can lead us to greater compassion and respect for our environment.

Back in the Barbican’s main gallery, the visitor confronts the work of Simon Starling, the 2005 Turner Prize winner. His Island for Weeds was commissioned for Loch Lomond’s inauguration as a national park but was promptly cancelled when the organisers realised the media frenzy that might result if they paid for a floating island to home Rhododendron ponticum, a terrible invader of the Highlands. “It’s a weird relationship that they have with the plant up there,” says Starling. “Scottish calendars are full of pictures of the landscape dotted with glorious ponticums, yet they spend millions to get rid of it. It says a lot about how identity is created through landscape.” He consulted an engineer to devise his floating home for the plants, a piece of artificial land, where nobody could object to a rhododenron colony.

From Utah to the Rhineland to the Highlands of Scotland, the show raises intriguing questions about how a home environment shapes artistic preoccupations. It’s no surprise to find German artists at the forefront of thinking about environmental art because Germany’s tradition of artistic engagement with ecological thinking dates back at least to Goethe, although Joseph Beuys is the most famous modern example. Beuys cited the influence of Rudolf Steiner, especially on his concept of social sculpture, where the whole of society is one big artwork, with every citizen able to contribute. Visitors can see Beuys’s Honeypump at the Workplace (1977), which points to bees as the ideal community at work.

But in America, art engaging with the environment has different meanings. Robert Smithson worked entirely outside the studio but was no eco-warrior. Starling is a big fan of Smithson but points out: “Pouring tar down hills, and those bulldozers making Spiral Jetty, it’s brutal.”

Although crammed with playful invention, the question is whether a show of the wilful, singular work of contemporary artists can have any effect on our degraded environment or, as the catalogue says, “inspire solutions for our changing planet”.

Starling sums up his feelings thus: “Who knows what Al Gore’s carbon footprint is, it must be enormous, but then he has changed the way we think about the world. It depends upon your sense of where the balance should be. There are people who are going crazy flying around the world preaching about global warming but to me, that seems like a job worth doing.” Starling’s rhododendron island is a startling, plasticky, experimental, funny and provocative piece of art; if it makes you turn off the lights more at home, so much the better.

Radical Nature: Art and Architecture for a Changing Planet 1969–2009 is open from Friday until October 18. www.barbican.org.uk

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