If you were casting for a film about a policy academic in Whitehall, and Nicholas Stern auditioned, you would reject him on the grounds that he looked so much like a cliche that he would be a caricature. If you were casting for the rock star of the modern climate change movement, on the other hand, he would be the last man in the world you would choose. Middle-aged, soberly suited, grey and compact, he speaks softly in the fastidious register of academia, comprised of paragraphs constructed almost entirely out of words such as "policy framework", "costs and benefits", "transparency of governance" and so on. Yet, when he speaks, the whole world now listens.

Since publishing the Stern Review in 2006, the professor has become the global authority on climate change. Commissioned by Gordon Brown, his study of the economics of climate change shifted the debate away from polar bears and unseasonal summers, and reframed it in the cold hard language of the balance sheet. Unless we invested 1% of global GDP per annum in measures to prevent climate change, the review warned, it would cost us 20% of global GDP. Suddenly, the CBI and the Institute of Directors were paying attention. It was a defining moment for the credibility of a movement once belittled as too counter-culture to be taken seriously. Stern became the grey hero of the greens - powerful precisely because he seemed such an improbable eco warrior.

Since then Stern has returned from the Treasury to the London School of Economics, been made a life peer, and is now about to publish a book - A Blueprint For a Safer Planet. Guided by three principles of effectiveness, efficiency and fairness, it calls for an investment of closer to 2% of GDP, with rich countries leading the way in emissions reductions. Proposing green technologies, international emissions trading, and financing to halt deforestation, it lays out the terms by which he believes we can avert catastrophe - and as such is fundamentally hopeful.

But Stern navigates a delicate path between optimism and Armageddon, and at a recent climate change conference he was still exhorting world leaders to grasp the magnitude of the crisis. "Do the politicians understand just how difficult it could be?" he appealed. "Just how devastating [a rise of] four, five, six degrees centigrade would be? I think not yet." With hindsight, he says he fears that even his own review underestimated the risks we face.

"When it came out, people thought I'd over- egged the omelette. But all the things people were looking at turned out to be worse than they thought. Doing nothing looks even more reckless than it did even a few years ago." He pauses, as if uneasy with such an intemperate word, but keeps going. "Recklessness is the only word. I mean, we have to recognise the scale of the risk. If we go on at anything like business as usual, we'll be at concentration levels by the end of this century which will give us around a 50-50 chance of being above five degrees centigrade relative to, say, the 19th century. We humans are only 100,000 years old. We haven't seen that for 30 to 50 million years. We haven't seen three degrees centigrade for three million years. The idea that humans can easily adapt to conditions like these ..." He lets the proposition tail away, too foolish even for words.

"What will we do? We'll move. People will move. Why? Because much of southern Europe will be desert. Other places will become underwater. Others will be hit by such severe storms with such frequency that they become almost uninhabitable. So hundreds of millions of people will move. You're already seeing people moving in Darfur, where droughts devastated the grazing land of pastoralist people, and they moved, and come into conflict with people in the places they're moving to. We're seeing that already on just a 0.8 degree rise. We're the first generation that has the power to destroy the planet. You're re-writing the planet. So you can only describe as reckless ignoring risks like that."

At the heart of Stern's work is a simple calculation. If the science on climate change is right, the transition costs incurred by switching to a low-carbon economy will - however daunting - be a fraction of what we will save by averting disaster. If the science is wrong, and we incur those costs unnecessarily, they would be "very far from disastrous", and we would still benefit, "because we will have a world that is more energy efficient, with new and cleaner technologies, and is more biodiverse as a result of protecting the forests". The logic of the argument is compelling, but is there any part of Stern that believes the science could be wrong?

"It's very, very remote," he says slowly. Less than one in 100? He looks surprised. "Oh, much, much less." The puzzle must therefore be why anyone would still doubt it. Nigel Lawson, for example, dismissed his review as "fraudulent", and published a book last year disputing the entire scientific premise of climate change.

"As an undergraduate, I did maths and physics. That doesn't make me a scientist," Stern responds, with exaggerated patience. "So I try to read and understand and talk to scientists. I'm staggered by how many people who are lawyers, or politicians ..." Or former chancellors? "For example," he agrees drily. "Taxi drivers. People behind bars. People cutting hair. They all seem to be knowledgeable and expert on the science.

"In public policy we have to understand a little bit about nuclear physics, and biochemistry, and genetics. So what do you do if you want to understand about genetics? You talk to a geneticist. You don't turn to taxi drivers or politicians. Both respectable professions, but you don't go to them for the science of climate change, you go to scientists. And what do you hear? That this is basically simple physics. It's not as if it's something strange or mysterious that people can't explain to you. It's not something outside the experimental. The greenhouse effect is something you can observe experimentally - and most people have observed the greenhouse effect themselves, in greenhouses. Yes?"

Does Stern feel angry with sceptics - or, as he calls them, irrational optimists? "Well, they're marginal now," he says with rather withering indifference. When he finds himself sitting next to one at a dinner party, does he even bother to argue? "I still believe in rational argument and communication. It's our duty to try. But it is an area in which people can be deliberately destructive," he says disdainfully. "There's a kind of yah boo argument: 'Don't believe it, don't believe it, don't believe it.' Or using language that's slightly more colourful, like that Paul Whitehouse character who said bollocks to everything. That's the kind of thing. It's yah boo stuff."

Stern suspects their perversity is ultimately down to political prejudice. He has no patience with those on the right who assume climate change is just a Trojan horse - an excuse for the left to interfere in the market. "This is about trying to help markets work. This isn't anti-market, this is about making markets work well. My position is pro-markets and pro-growth - not anti-growth. Indeed, it's ignoring the problem that will kill off the growth. High carbon growth kills itself. First on very high hydrocarbon prices, but second and, of course, much more fundamentally, on the very hostile physical environment it would create."

But he has even less time for those on the left who think climate change is "an elitist hobby horse"; a distraction from poverty in the developing world. "We will not overcome world poverty unless we manage climate change successfully. I've spent my life as a development economist, and it's crystal clear that we succeed or fail on winning the battle against world poverty and managing climate change together. If we fail on one, we fail on the other."

When we meet in his book-lined office at the LSE, Stern has just returned from breakfast with his old friend Mervyn King at the Bank of England, and I get the impression that he suffers any less cerebrally rarefied company with weary forbearance. Oxbridge-educated, 62, he has worked at the European Bank for Reconstruction and Development, the World Bank and the Treasury, but "I am a public policy analyst, that's who I am," he says more than once. He seems intellectually and temperamentally ill-suited to the rough and tumble of political knockabout, for to speak in a language the rest of us can understand seems a challenge - if not a chore - at times.

Sometimes, though, I suspect he deliberately obfuscates. It was Brown who commissioned Stern's work on climate change - yet the prime minister subsequently authorised the third runway at Heathrow. When I ask if Stern supported that decision, his reply is somewhat opaque: "I was uncomfortable with the way that decision was structured." I would have thought he'd have been furious about it. "Well, no. I was worried about the framework for the analysis." What does that mean? "I felt that the analysis should have been done in the context of an overall strategy." Surely, I press, given the urgency of the situation, and the authority his voice would carry, he had a responsibility to speak out? "I don't want to get into having to take a running position on each individual project and proposal. You have to keep it in that overall perspective and we shouldn't turn it into a symbolic argument over one particular thing." Politics is symbolic, though, isn't it? "Yes, but I'm not a politician giving a running commentary. I'm a public policy analyst."

At other times I wonder if he understands the way less rational or educated minds work. On policy analysis he is quite brilliant - but on the politics of the real world he can seem almost naively high-minded. For example, his book highlights the imperative of halting deforestation, but says relatively little about the problem of corruption in developing countries where the issue applies. Clearly, the west needs to divert some of its wealth to them, to deter deforestation. But taxpayers complain that Africa is corrupt, and that they've already spent decades sending aid that went straight into the pockets of officials. Why should they send more money if it won't stop the forests being destroyed but will fuel corruption - while they're being told they can't fly off on holiday whenever they like?

"Yes, but that's based on a misunderstanding," he says, looking irritated. "Progress in Africa over the last two decades has been much, much stronger than the preceding two decades. If you ask those people to tell you how many sub-Saharan Africa countries there are, and what their growth rates were over these last four decades, they wouldn't be able to tell you. They wouldn't have a clue." I'm sure they wouldn't - but that seems beside the point.

Similarly, although he talks hopefully of a World Environment Organisation, he puts surprisingly little emphasis on coercion. Won't we need some sort of equivalent to the International Criminal Court to enforce international agreements? "People have to ask themselves, if I transgress as a country what would be the implications for me and for the coalition that's dealing with this problem? You'll have to think about the consequences of your actions. If a big country pulls out of this they can't simply say, 'Well everyone else will do their bit.' They have to ask themselves what will happen. It will be the politics of particular countries. People will demand that their governments behave responsibly."

Ultimately, he points out, the choice is quite simple: however difficult the challenge of action may be, the alternative is unthinkable. "If you say I'm not going to do that, what's left? What's left is you just reach for the suntan lotion and the big hat, and you say it's all too difficult, I'm signing off on this, and let's all fry. Why would you want to go there?" It seems more or less unimaginable to Stern that people would be stupid enough to allow a catastrophe to unfold, and his ultimate message is one of optimism.

"There are so many ideas out there, the pace of technological progress is so fast. It's a very optimistic thing about human nature; when humans focus on a problem, they're quite ingenious. And we have to recognise that this subject is young. It's only been deep in our understanding for two or three years. The scientists, of course, have been thinking about this for a long time, but in terms of politics and policy it's been big only for two or three years. I think if you look at it in that context, let's recognise what the government has done. We're ahead of the world on climate change legislation. I think the climate change bill is broadly along the right lines. If you ask yourself the question, 'How far have we got?', we've got a long way. It has to be faster, but let's not fail to recognise how far we've come."

Not even the world recession has dampened his optimism. "This recession is seen as something that would prevent action on climate change only if we confuse ourselves. If we think clearly, this is an opportunity to bring forward some of those investments, because resources are a bit cheaper at the moment. I've been struck that this climate change story has stayed very much on the agenda, the way that the green stimulus has been seen as part of the expansion package. In the next two or three decades, I think low-carbon technologies are going to be like the railways or IT - big drivers of growth."

Stern won't live long enough to know if the world takes his advice. But if he had to go to the bookies now and place a £1,000 bet on whether we'll manage to do what's necessary in time, which way would he put it? "I would bet," he says cautiously, "we'll get there. But as in any bet, there's a risk of being wrong".

'There are many half-baked attempts to naysay the science, but they always unravel on inspection'.