Heatherwick's remarkable talent carries a specific hallmark: a kind of sensuous lateral thinking which produces bold sculptural forms using highly unlikely materials. His latest project, the Lottery-funded creation of a new pedestrianised square in Newcastle, is a typical rabbit out of the hat.
He's going to cover it with a specially developed blue-chipped concrete, rucked up around trees and walls as if it had been laid by a dodgy carpet fitter. And under it, part-glimpsed through thick glass slabs set into the surface, will be a peculiar underworld crammed with art objects and chunks of ancient foundations.
The Newcastle project is Heatherwick's first large scale work, but the boldness of its concept is nothing new. When he was commissioned by Harvey Nichols to produce a window display that would become the focal point of last autumn's London Fashion Week, the 27-year-old's response was brilliantly outrageous: he devised a massive and fiendishly difficult continuous sculpture like a whacky stretch-pretzel running in and out of the ground floor display windows.
And it wasn't just the jeunesse doree who were impressed. When Heatherwick returned to check the condition of the extruded polystyrene and wood-veneer sculpture a week after its installation, a couple of laddish diamond geezers happened to stop in their tracks near him to peer upwards at it.
"'kin `ell," murmured one of the accidental critics, who looked as though he'd just been terminally Tango'd.
"I reckon it's meant to be a Twiglet," mused the other. And there was a grain of truth in this, for everything that Heatherwick has created since picking up his MA at the Royal College of Art in 1994 is surprising: he seems to operate in a Twiglet zone of expression where only startlingly original and flowing solutions are allowed.
The Harvey Nichols commission is simply the latest example of this imperative. It took months to design and prefabricate in a factory loaned by the Docklands Development Corporation, and a week of nights to erect, with an increasingly dazed team of nine led by his collaborator and project manager Jonathan Thomas.
Prompted by the facade's strong vertical elements, his response was to make a sculpture which was "like the weft in weaving which weaved in and out of the windows".
It was a simple concept which Heatherwick immediately, and typically, developed into a hugely taxing physical and technical process. For him, designs are touchstones and, somehow, he will find ways to achieve them.
Step one was to make a precise one-twentieth scale model of Harvey Nichols's Knightsbridge elevation. He then, without the aid of prepared drawings or even sketches, hand carved each snaking, variably-dimensioned element of the stretch-pretzel from polystyrene. When he was satisfied, his staff reproduced the elements from the originals, but 20 times bigger.
How, though, to translate the shapes of the small originals into precise, but much larger, copies? Heatherwick's solution was an extraordinary admixture of logic and craft skills. He laid every one of the original pieces on to graph paper and marked their three-dimensional co-ordinates, which ran into more than a hundred individual drawings. He then drew out a larger, re-scaled graph on the floor of the Docklands factory. The pieces were carved to actual scale from polystyrene and checked on the chalked-out co-ordinates, then faced in birch veneer less than 1mm thick. From start to finish, the process took the best part of five months and left his studio looking like an arctic ice floe.
Heatherwick tends to operate like this, rarely bothering to detail his work in advance. The result has been a use of materials in relation to form that has, quite accidentally, pushed the envelope of technical possibilities.
He set the trend early. The extraordinary 20ft gazebo he produced for his degree show was made of gapped plywood sheets and shaped like a melting X.
Terence Conran saw it and bought it on the spot. When Heatherwick set out to make it, he had no idea how it could be done, or if it would be weatherproof. "It's just two piles of plywood," he said. "The idea was to make them fall into each other." With advice from engineer Ron Packman, the 8ft x 4ft Finnish birch ply sheets were configured in 18 sections, with each section set on to locator bolts fixed into every third sheet. The result is a stunning and wholly delightful form, proof against any weather except driving rain.
Heatherwick's design for the Image Bank creative photography awards was literally a cutting-edge exercise. He took an obvious concept - winners' cups - and found a firm in Northampton, GFM, that would dare to cut a four-and-a-half-inch-thick block of stainless steel into 2mm thick "cutout profiles" in identical shapes which descended in size.
Laser beams were ruled out because the heat effects associated with it are too unpredictable on reflective material. GFM used ultra-high-pressure needle jets of water controlled by a computer program based on Heatherwick's drawings. The cutting process, which could not be stopped for checks, took 26 hours. The pieces slid out almost perfectly, in places separated by only a few microns.
Polystyrene, plywood, steel. Even corrugated cardboard cannot escape the gravity of the designer's Twiglet zone. Commissioned last year to come up with a starkly unusual window display medium, he suddenly thought of cardboard; several weeks, and nearly five kilometres of the stuff later, the windows of London's Conran Shop were a swirl with convoluted waves of it, with products displayed in layered clefts.
The genesis of Heatherwick's creativity can be traced to his primary school. "The school I was at had concrete posts around it with wire mesh fencing," he recalled. "I got bits of small branches and found that I could rub it against the wire to carve it. I suppose I was eight."
But the touch paper was really lit when he was taken to craft fairs by his mother. "I saw people making bows and things," he said. "There was a wonderfulness to things being made - a raw wonderfulness."
These crafty stimuli fermented and by 1993, when studying art at Manchester polytechnic, he suggested in his dissertation that, while every three- dimensional object is sculpture, "sculptures kept in galleries where you are not allowed to touch them might as well not be objects at all, but holograms ... touching an object and experiencing its materials is a vital part of understanding it, and something that fine art actively discourages."
Heatherwick advertises his condition unmistakably; verbal explanations are invariably accompanied by hand actions, as if he can't help trying to make what he's talking about, get it right by manipulating the claggy clay of an idea with his fingertips.
He can't help it. Heatherwick's early test pieces prove it: a curved funnel flanged with sails, formed with veneer strips; a bouquet of white buds soft-sunk in snow, formed from a single piece of linen; a swirl of wires linked with bands of plastic electrical connectors, giving the effect of a Red Arrows formation stunt.
His designs have at least two trademarks: they are invariably surprising in terms of materials and form in relation to their final context; and they have a wonderful quality of flow and movement: inner surfaces flow into outer surfaces; thrust segues into withdrawal and withdrawal might accelerate into outward movement. It's all about revealing transformations.
Much of his work is seamed with accident and as far as he's concerned it's pure holy water. "You can spot them and say `More of these accidents!' There's always this possibility with live objects. It's a shame when things are so theoretical." The trick, he suggests, is to create opportunities for accidents.
And speaking of avenues, Heatherwick's Newcastle project is literally poised to give him street cred. As usual, his proposal was extraordinary. But here's the real surprise: "When you need a seat, you just fold it up from the carpet." There's more: "Beneath the carpet is an underworld. Where a seat is folded up, beneath it will be a layer of glass and under that you might see a bit of the old city wall, or a painting from the Laing Gallery." Patterns of fibre-optic cables will also be fed into the seats or other rucked-up areas to create a delicate field of stars: Heatherwick thinks of them as "glittering grass seeds".
In another Lottery-dependent project, he has been commissioned by the Science Museum to design a house to display several hundred materials. He came up with a delightful solution: a flowingly contoured cavern of delights in which each of the contours - imagine looking at closely-spaced elevations lines on a large scale map of Snowdonia - is made of a different material.
Thomas Heatherwick is clearly a designer ready for even bigger challenges. Pretzel logic and Twiglet zones are one thing, but he has other ideas. "A building," he said quietly. "That's my real dream."
And if anybody with clout, and wit, has any sense, they'll commission him to design the one thing that would put Heatherwick to the ultimate and defining test, and surely squeeze something truly amazing from him: an art gallery.