The voice comes from above: “We’re watering, fast and furious.” I should say so. Weather like this? Murder for lawns.

But you think your garden’s had it tough? Then pity poor Heather Ackroyd and Dan Harvey. Measuring 760 sq m, their lawn is exposed to winds as hot as a hair drier four floors above the Thames at Waterloo Bridge. And it’s vertical. In the name of art Ackroyd and Harvey have wrapped turf around the fly tower of the National Theatre in the hottest spring since records began.

“Can’t stop, can’t stop,” gasps Ackroyd, as she scampers breathlessly up and down the scaffolding like a mountain goat, armed with the mother of all hosepipes. One errant delay and some of her estimated 1,875 million pregerminated grass seeds will wither, caught in the grip of the vicious sun pouring through chinks in the scaffolding. “Look here, it’s baked solid,” she calls to Harvey, two floors down.

Last week the pair and 20 friends spent four days daubing the fly tower with seven tonnes of ceramic clay, strengthened with fibres, before pressing fistfuls of seeds into the “soil”. Harvey shows me his hands, chalky with clay, gnarled with calluses, cracked with cuts. “We caressed every inch of this building,” he laughs, “and look what it did to us.”

Then the hard work began. For the past week they have watered the tower incessantly to make the seeds sprout. “There were two types of weather we feared,” Harvey says, “torrential rain, to wash the clay away, and hot and dry. Guess which we expected?” It takes an hour and half for the remaining half dozen workers to water the tower from top to bottom. By the time they finish, the top’s dried out and it’s time to start again.

Harvey continues watering alone until midnight, long after Ackroyd has headed home with the commuters to Dorking to feed and water their other project, their nine-year-old daughter Adele. Harvey sleeps a couple of miles away, but he’s up several times during the night to give the grass a drink. He looks exhausted, like a parched man after crossing a desert. “It’s the exposure up here in the sun. You start hallucinating, a bit hysterical after a while. I suppose it is a slightly strange thing to be doing.”

The pair have been grassing buildings since the early 1990s, when a mutual friend introduced the two artists with a peculiar obsession with turf. They began by seeding a derelict building in an Italian hilltop village. Since then they’ve grassed art galleries, a theatre in Zurich, a mausoleum in Riga, their own living room, the interior of a church in southeast London; they even create detailed grass “photographs”, after noticing how variations in sunlight trigger different degrees of chlorophyll in the blades.

The National, though, is their biggest project to date. “We used to pass the theatre on the 59 bus home when we lived in Brixton,” Ackroyd says. “We’d look out of the window and think how enigmatic, how aggressive, how gloriously uncompromising it was. Wouldn’t it be great to . . . nah, impossible.”

Until they got a phone call from the theatre director Katie Mitchell asking them to do just that. “We worked with Katie ten years ago on a Strindberg play,” Ackroyd says, “and she told us of the opening line of his A Dream Play – ‘Look how the tower has grown’. Apparently Strindberg had an hallucinatory attack while crossing Waterloo Bridge during an abnormally hot summer in 1893.”

Ackroyd and Harvey see their work as the latest in a long line of artists doing strange things to buildings that stretches back decades through the Situationists to the Dadaists and surrealists via Christo & Jeanne Claude and Gordon Matta Clark. For Ackroyd, trained in drama, it’s not the growing that appeals but the “theatre” of grass: not just the spectacle, but “the life force, that sense of a million tiny dramas literally unfolding inside each seed, but here on an epic scale, on stage for the world to see. When each blade of grass emerges, it’s like a baby groping for the light, very strong, full of growth. Its growth, maturity and eventual death is theatre.”

The grass is indeed sprouting delicately, like a six-o’ clock shadow. A day later and it’s a buzz cut. By the time of the opening on Thursday it should be a luxuriant fringe; next week a Hugh Grant floppy mop billowing in the breeze. For Harvey, who studied sculpture under Cornelia Parker, it’s these shapes of nature’s growth that attract. The electric green extraordinariness of ordinary, overlooked grass is exposed by its juxtaposition with the National’s dun-coloured concrete. In turn the gruff 1970s brute, which its architect Denys Lasdun always envisaged as a metaphorical landscape, chiselled into strata, is rendered soft, squidgy, sensuous, luxuriant and organic in its grass coat.

This vivid jolt of nature in this most thorny, most artificial, of grounds has obvious resonance. The pair are horrified by the divorce from natural rhythms that city-dwellers experience; they blame it for our tardiness to awake to climate change, the biggest of “epic natural dramas”, which has animated them since its discovery in the 1980s, and whose recent rise up the political agenda has added a new pointedness to their increasingly activist work. In 2004 they travelled to the Arctic with Cape Farewell, a group that unites artists, writers and scientists to raise awareness of climate change. Their next project is with the valiant eco-architect Bill Dunster, famous for his BedZed estate in South London.

“If the grass does wither in the sun in the next month,” Harvey says, “then it makes our point perfectly on the biggest, most unmissable of stages. Look how little it takes to f*** up this thin skin of life.”

Fly Tower is at the National Theatre from Thursday

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