Thomas Heatherwick on London buses, hairy buildings and a 180ft-tall KerPlunk

And more than that, he's original in all of them too. Here's an inventory of just a few things he has made or designed in the past 20-plus years. Chairs made out of glass. Another chair that looks like a bit like the face of a shar pei dog. A bridge that curls up when it's not in use. A bag made out of zips for Longchamp. Longchamp's flagship store in New York. A new entrance for Guy's Hospital that ripples like a steel eggbox. A public sculpture for Manchester that resembled a mutant sea urchin, or maybe an alien spacecraft setting down beside what is now Manchester City's Etihad Stadium. A cafe on Littlehampton beach that looks like a sea-worn pebble. Watch straps made from fibre-optic cables. A church in Sussex. A hairy building for the World Expo. The new London double-decker bus. A power station. Oh, and Christmas decorations for Boots.

Heatherwick – the Scottish name comes from a grandfather who was in the Scots Guards – is a curly-haired, softly spoken geyser of enthusiasm who's currently having a very big year. By December – all testing being satisfactorily completed – 600 of his London double deckers will be let loose. Come the summer we'll finally get to see his design for the Olympic cauldron. He's not allowed to talk about it but does say it's not just about the cauldron itself. It's also about the moment that leads to the cauldron being lit by the Olympic torch. He's working on that with Trainspotting and Slumdog Millionaire director Danny Boyle.

While we wait for all that, there's also a huge retrospective exhibition at the V&A in London as well as a huge brick of a book entitled Thomas Heatherwick: Making, which gathers all the designs he has come up with (some made, some not) since 1989.

I'm disappointed, I tell him when we sit down to talk in his studio near King's Cross, that it's not a pop-up book. He smiles as if to say the idea – or something wilder – had crossed his mind. "If we turned the book into a project it would triple in cost, and I wanted this to be something a mum might buy her 14-year-old child who's interested in ideas and doing things."

He has something of the eager teenager about him, actually. But the truth is he's 41, lives with his partner and their young twins and runs a studio that is home to 75 staff and a rising reputation. What's interesting, though, is that there is no signature Heatherwick style. There's no obvious stylistic tic or material foible that marks his territory, no Heatherwick equivalent of Frank Gehry's trademark metallic waves or Santiago Calatrava's organic curves and swerves. For Heatherwick it's all about the "importance of particularity".

"I don't have a sense that my role or the studio's role is to do Heatherwick projects all over the world and make our mark," he tells me, his voice quiet but eager. "I feel our job is to bring into being a special project. But its priority is to be a special project for that place. It almost feels the most disrespectful thing to stamp your style on different places all over the world. The greatest respect you do is to do your best new work in that place influenced by that place and root it. I'm wary of the way very similar things are happening all over the world."

Ask him for his design heroes and he starts talking about the great Victorian engineer Isambard Kingdom Brunel. "He was designing bridges, ships, new rail gauges, railway stations. There was nobody trying to slip him into a box."

As he talks I look around at the objects he's gathered in his studio. From my seat I can see a stetson, rocks, candles, raised maps of European countries on the wall, a light shaped like a lighthouse, animal horns, a blown-up model of a desert crystal, a coco de mer nut (you know, the one that looks like a bottom), Becky "Friend of Barbie". Natural and manmade designs that speak of individuality rather than the construction line. Beside us sits an extruded aluminium bench. A Heatherwick design. It glitters and shines like the future. But before that it's time to travel into the past.

Thomas Heatherwick was brought up in north London in a family full of high achievers. His maternal grandfather was a poet and a Spanish Civil War veteran whose own grandfather had started the fashion line Jaeger. His maternal grandmother, meanwhile, sounds the most amazing woman, a German Jewish refugee who had known Carl Jung in Berlin, fled to London before the Nazis could seize her, set up and headed Marks & Spencer's textile design studio, worked for the architect Erno Goldfinger (inspiration for the Bond villain), then retrained as a psychotherapist and returned to Germany after the war to work with the children of the Nazi era. "She wasn't the cosy image of a British granny who made you cakes," says Heatherwick, which is a bit of an understatement. "Sure, she fed you in a big way, but when you were walking with her and the road was curved she walked in a straight line. So you were off the pavement and chasing along behind her trying to make sure a car didn't splat her." Her work ethic was ferocious and that rippled down through the generations.

His mother is a jeweller and enameller and an expert on beads who had her workshop in the family home. She would take Heatherwick to craft fairs where people would be making hammocks, thatching and drystone walling. "My father was giving me the antidote to all that, which is probably why they split up when I was 14. He was taking me to see Milton Keynes, this new town, and houses of the future exhibitions."

He was experiencing everything from handmade to high tech. Perhaps it's no wonder then that design was the obvious career path. "I feel like it's a boring story to tell because there isn't a moment of rejection and revelation. I feel in some ways I'm a really obvious outcome of the influences that were put into me."

Heatherwick went to Manchester to study three-dimensional design at the end of the 1980s. The city was still a mash-up of Victorian grandeur and bombed out toothlessness then. But these were the Madchester days. By day he'd study, by night he'd head off to the Hacienda nightclub. "It was one of the most exciting times in my life," he says. "The city felt full of potential and even the tutors were a young collection of recent graduates themselves and had a sense that their pupils could do all sorts of things."

Heatherwick decided to do a building. Not a model of a building but an actual building. Even though the polytechnic had an architecture department nobody had done that before. He found £20,000 worth of sponsorship, more than a mile of Velcro to hold his polycarbonate structure together and he built a pavilion. That seemed more worthwhile than doing a drawing or constructing a model. Making remains key to him. He is by nature hands-on. Looking around at the desks of his colleagues he tells me he's very wary of what he calls "computeriness". "This is a studio. There's a laser cutter, a welder, chisels, computers. It's a place of making first."

If Manchester was to be the making of Heatherwick it was also almost the unmaking of him. Or his reputation at least. After returning to London to study furniture design at the Royal College of Art, he started making a name for himself through redesigning a city square in Newcastle and working with Mary Portas on a remarkable window display for Harvey Nichols that saw a plywood structure weave in and out of the shop front. He even designed an exhibition in Glasgow's Lighthouse for the Year of Architecture in 1999 using mostly clingfilm. Then in 2002 he was commissioned to create a commemorative sculpture in Manchester for that year's Commonwealth Games. He came up with such an audacious concept that suddenly his name was in the news pages. A hedgehog of 180 steel spikes, entitled The B Of The Bang – and known locally as KerPlunk after the children's game – was Britain's tallest sculpture when it was built. Unfortunately it arrived two years late and twice the planned cost. Then days before it opened one of the spikes fell to the ground. Fears grew that it was a danger to the public. It was taken down in 2009, four years after completion, much to Heatherwick's despair.

"When you do something new there are bound to be teething problems occasionally. It's down to how much confidence there is in a country to say, 'Let's solve this.'" He mentions Anish Kapoor's Cloudgate sculpture in Chicago, a construction that also had teething problems and ended up costing more than five times its $3.5m budget. "But the city dealt with it and it's phenomenal. It's a centrepiece of the city's regeneration."

When the B Of The Bang's problems started, he says, he considered chaining himself to it. "People have said it's down to all the cutting-edge technology. But it was made from lamp-posts! There was a technical problem with it and it was solvable. It just needed to be resolved. But there's a political climate in Britain that's very scared of media criticism and there's a media that loves a good sneer -" He trails off, the energy leaking out of him for a moment. "And that's part of our freedom - Yeah, it was very gutting." Listening to him talk he's obviously still agitated about the project's failure. Words tumble out of him at an even greater speed than normal in his desire to make me understand. But in the end, he says, it wasn't his project, it was the city's, and the fate of it was theirs to decide. "It's just so sad. And I really wanted to do something for Manchester, the city that had given me so much."

The papers reported that his studio had to pay Manchester City Council £1.7m but he says now that because there was a whole host of contractors and sub-contractors the studio "did not have to pay out much at all" in the end.

"As designers of projects, often you get too much credit. There's a team of people who make projects happen and that includes manufacturers. But in communication terms it's tidier to focus on one person." He says he's always had too much credit for his successes and maybe with B Of The Bang he had too much of the criticism. "But your role then is to have a broad back."

Disappointing as it was, it didn't stop Heatherwick. Three years later his studio was commissioned to build the UK Pavilion at the World Expo in Shanghai, a chance to represent Britain to the world. "There were 250 pavilions and the British Government said, 'You've got to be in the top five,' and that was the brief, really. Then they said, 'But we're giving you half the money of the other western nations.'"

The worst thing they could have done, he says, is build something cheesy about red telephone boxes, the royal family and Manchester United because that wouldn't have stood out. That would have been expected. "So the safest thing we could have done was build the world's biggest hairy building." And so they did, a pavilion seen by 70 million visitors, one covered in 60,000 acrylic rods, each of which contains a seed at the tip (inspired by the opening scene of the Harrison Ford movie Witness, it seems).

The Seed Cathedral – or the Dandelion as the Chinese called it – won the gold medal for pavilion design and led to new opportunities in the Far East for the Heatherwick Studio. He's now working in China and Malaysia. He is bringing British design to the world.

It's possible that Heatherwick represents something new in domestic design. Since the war, the dichotomy of British design has been between monumental modernism and twee domestic heritage. For so long the two trends were in opposition, with the latter usually winning out. "I grew up in London with the sense of resignation that these things happened in Paris or Barcelona. Those were the places you went to see the contemporary imagination applied to the environment. Milton Keynes didn't seem like it was cherished and valued. It was just seen as an oddity."

Design, it seemed, was made in spite of rather than because of the culture. But there were individual designers – Norman Foster, Richard Rogers, Terence Conran – who were able to impose their will and their vision and that has rippled out to the point where now we all shop at Ikea and we all want our own grand design. Heatherwick is a beneficiary of that change. "I think we are much further down the track now, which maybe leaves a space for people like me and my team to sort of spot a little gap and try to run for it."

He's been running hard for the past two decades and he's showing no signs of slowing down.

These days Thomas Heatherwick says he is more interested in designing buildings than teapots. "Absolutely. We have been working on the new London bus and you're aware that it has, in a way, more impact than any single building in London. A bus is part of the landscape of London, the architecture of London.

"I'm interested in all the jigsaw pieces that help make cities more particular and less like other cities."

After the interview, I find myself walking around London wondering what a Thomas Heatherwick city would look like. Like nothing else, I guess. Like nothing else. n

Thomas Heatherwick Making is published by Thames And Hudson, priced £38. Heatherwick Studio: Designing The Extraordinary opens at the Victoria & Albert Museum in London on Thursday.