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This week, contractor Cleveland Bridge UK is due to start installing the passive damping system intended to correct the Millennium Bridge's sway, almost exactly a year after the crossing was opened and rapidly closed again.

Right from the start, Wise knew that the bridge, which relied on untested engineering principles, would be risky. "When we first came up with the diagram, the single line across the river, we were thinking, crikey, that might be too far out on a limb," he says.

But his casual demeanour disguises the fact that Wise is someone who thrives on placing himself in risky situations. He lists his hobbies as "rock climbing, mountaineering, snow and ice climbing"; his lean physique is what you'd expect of someone who enjoys hanging from precipices. And in 1999, he took the biggest leap of his career: walking out of his partnership at Arup just as he was establishing himself as the most outstanding engineering talent of his generation – and just before construction work started on the bridge.

Eight years ago, at 36, Wise became the practice's youngest-ever partner and was honing his abilities on structurally innovative projects such as Nick Grimshaw's Waterloo International Terminal and Richard Rogers Partnership's Channel 4 headquarters.

The Millennium Bridge was very much his own idea. Wise is keen to correct the popular misconception that the design was a multidisciplinary collaboration, pointing out that only he and fellow Arup engineer Roger Ridsdill Smith were present at the now famous napkin-sketching session that gave birth to the "blade of light" concept.

"I get really annoyed when I read in the paper that Norman Foster and Tony Caro sat in the same wine bar on the night that Roger and I did the first sketches," he says. "Because I don't think Norman's ever been in a wine bar."

Then, to the utter surprise of everyone, Wise left Arup on the day the last package of drawings was handed over. He says he had no idea what he wanted to do beyond making a change in his life. "I wanted to move on and develop," he says. "I told Arup I wanted to take some time off and I didn't know if or when I'd be back."

His decision was also partly the result of a feeling that Arup had lost its initial idealism. "Previously, social responsibility was higher up the agenda," he says, citing cigarette factories in Russia and coal-fired power stations in the Far East as examples of the type of project the firm would not have contemplated in the past.

He considered travelling to Spain to indulge his passion for flamenco guitar, but finally decided instead to form his own engineering practice, Expedition, with two colleagues he took with him from Arup, Chris Smith and Sean Walsh.

But his departure meant an end to his involvement with the Millennium Bridge – until 10 June last year, when he took his young son Tom to the opening ceremony. Wise admits he briefly feared an engineering disaster was unfolding beneath his feet as the sway grew increasingly severe. "The first time it happened, it was scary. There was a passing thought of, 'shit, I hope we're not going to all end up being shaken to bits here'."

He immediately offered to help his old Arup colleagues, many of whom were also on the bridge trying to figure out what was going wrong. "They said no," he says. "I really wanted to sort it out, but there was no way Arup would let me, because if it did, that would reflect very badly on them – that they couldn't fix it themselves."

Wise had to watch from the sidelines as the cause was identified and a solution developed. He is upset that the aesthetic purity of the structure will be compromised by the addition of dampers, particularly the struts attached to the piers, which he says are "fundamentally at odds" with the concept of the deck "flying through without touching the ground".

He is both humble and unapologetic about the design and its unfortunate flaw. "There's no question the sideways wobble is something we got wrong. But I think with hindsight we wouldn't have treated it any differently. Obviously we could have designed a bridge that wouldn't have wobbled – a really tough, heavy, traditional bridge – but if we did that we wouldn't have had an iconographic piece that everybody could enjoy but just another piece of turgid fancy."

At the same time Wise is excited by the engineering possibilities opened up by the bridge – and the solution to its wobble.

"I think the bridge is a sort of stepping stone on the way to a more responsive, more reactive sort of engineering. You can create a very light structure, and then control the way it behaves afterwards. Arup's fix is a passive control but I think the next generation will have active control – tiny servos controlled by software. You can imagine a very light building that, as the wind blows, responds and pushes the other way, or a bridge where the tension increases as more people go on it. It goes against every single engineering principle we get taught at university."

The wobble has not affected his career, he says; Expedition is busy with projects for architects such as Michael Hopkins, Chris Wilkinson and Richard Rogers. Wise is now working on his first bridge project since the Millennium Bridge – a lifting pedestrian crossing in London Docklands, featuring two pivoting arms that swing from horizontal to vertical to allow ships to pass through. "It's like a pair of scissors," he says, adding: "We were interviewed for the job the day after the bridge wobbled. The client was really excited about it even though it wasn't working."

Wise, too, evidently feels the same way. "It's a shame it wobbled quite so much, but I love the fact it did because it's alive and it has personality and spirit. It looks like it should move – and it does."