Earnest young men with deliberately messy hair, designer spectacles and cutting-edge backpacks throng the lobby at Arup. On the wall is a colour projection of some of the engineering firm’s latest projects, work that has had the world’s architecture critics drooling — the bird’s nest Olympic stadium in Beijing, the Second Avenue subway in New York, London’s Gherkin building — and some subtle plaques reminding visitors of past achievements, such as the Sydney Opera House and the Pompidou Centre in Paris.

This is clearly a cool place to work. Feeling awkward in a suit and tie, unfashionable spectacles and hair that I really wish I had had cut last weekend, I am taken up to meet the king of cool, Arup chairman Terry Hill. And, thank the Lord, he looks like a provincial bank manager.

Not that I expected Hill to be an ageing groover, a Sir Mick Jagger of engineering. The 60-year-old Lancastrian, who has run Arup for four years, cut his teeth building roads and railways in Britain, Africa and the Middle East, not an environment in which a dandy would thrive.

Tall, with black hair, a ruddy face and owlish glasses — perhaps the boys downstairs could advise on some funky frames — Hill exudes solidity and, suitably for a career engineer turned manager, is precise and fluent in expression. He is just the kind of person you can imagine a politician turning to for advice when yet another plan has gone pear-shaped.

They have done. Hill and his fellow Arupites are old hands at the big politics that go with big projects. They were the behind-the-scenes movers and shakers on decisions that shaped the face of Britain over the past two decades.

Remember Margaret Thatcher’s mid-1980s plan to build three orbital roads for London, Ringways 1, 2 and 3? Thought not. Hill helped kill it. Remember the British Rail scheme to bring the high-speed rail line from the Channel tunnel carving through the south London suburbs? No? Hill and his merry men killed that too.

Now Arup has another cunning plan, a £4.2 billion extension of the high-speed line. It would run west of the capital to a new mega station near Heathrow, kick-starting new rail lines to the north, and perhaps removing the need for the airport’s third runway. Hill went to see transport secretary Ruth Kelly about it last week.

Challenging convention has made Arup what it is, says Hill. “Thatcher wanted to identify the next generation of motorways for London, and we did some work on it for the government. But in a typical Arup way, we refused to accept the question. Instead we asked — what is the problem?”

The process was repeated with the Channel tunnel rail link, where Arup had to see off British Rail and then get political backing for its own alternative route through east London. Cannily, Hill won support first from Michael (now Lord) Heseltine, then from John Prescott. It was a high-stakes game, one that helped shape the company. “We learnt an awful lot. When we went into it we were a consulting engineer, but in the process we transformed ourselves into something broader.”

It’s not difficult to imagine a politician feeling comforted by Hill. His conversation is peppered with touchy-feely phrases that might have come straight from the Tony Blair book of management. Arup is “a fertile place to grow new things”, he says. Its staff have “freedom, and accountability” and the company has “a responsibility to society at large”.

A look at the firm’s history tells you where the new-age speak comes from. Arup is an unconventional operation. It employs 10,000 people round the world and turns over about £750m a year, yet has no shareholders — at least not in the conventional sense.

It was set up in 1946 by Sir Ove Arup (a Danish engineer by whose full name many people still know the firm) and made its name in structural engineering, particularly for landmark buildings and bridges. Arup were the people who turned the architect’s flight of fantasy into reality, a skill demonstrated at the projects in Sydney and Paris. Sir Ove died in 1988. By that time the firm had already spread its wings beyond pure engineering into all sorts of other professional services. Arup will still do the structural engineering or the wiring for your new skyscraper — but it will also plan your new city, design your new high-speed rail line or nuclear-waste repository, and help you find finance for it.

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