In his music, Jarvis Cocker has always been a social commentator. Now he's become an agitator. Lucy Siegle talks to the Arctic's new defender about the oil hunt that threatens the world, the joys of "rascality" – and whether he regrets mooning Michael Jackson.

Jarvis Cocker sits with unblinking patience as syringes of salt and sugar are applied to his beard and hair and he is transformed into a frosted Arctic explorer. He blinks through his famous glasses and feigns shivering for the photographer. It's the kind of good nature that we've all come to expect of Jarvis, and that's made him a "national treasure". "It's good that I managed to hoodwink so many people," he says. "I am actually not that nice a person."

I smile indulgently, but actually I don't believe him. Can he give an example of a recent tantrum or piece of bad behaviour? "Yes, Brixton this month. Steve [Mackey], our bass player, shouted at me during a Pulp gig because I was nasty to Mark [Webber], the guitarist, on stage. He told me off. He was right to. He said: 'You're the one with the microphone so nobody else can answer back.' I blamed it on these steroids I'd been taking for a lung problem. I'm a nasty piece of work."

Then he tells the special effects make-up man not to worry about the mess on his tweed jacket. It'll brush off, and anyway he's brought a spare shirt. It's not convincingly nasty. But we are about to see another side of Jarvis: as a (softly spoken) ambassador for the environment. Greenpeace is preparing to launch what it hopes will be the ecological campaign of our generation, and Jarvis is the frontman of the UK part. As you may have deduced from Jarvis's iceman get-up, this seminal campaign concerns the Arctic, which is losing ice and gaining unwanted attention. Temperatures in the region are rising faster than anywhere else on earth, causing the ice cap to melt. Scientists think the North Pole could be ice-free in summertime within 20 years.

As the ice melts, Arctic and non-Arctic nations alike are appearing, like vultures in snow shoes, determined to carve up the spoils. That includes the potential for fishing in the newly thawed Arctic Ocean and 90bn barrels' worth of oil beneath the melting ice. No matter that this is just enough to keep the world going for a paltry three years – behind closed doors, nations and multinationals are still planning to carve up the Arctic for their own ends. Don't you just love humankind sometimes?

Greenpeace will call for a moratorium on Arctic exploration of this type and fight tooth and nail to resist ownership of the Arctic, arguing that it must be a global commons – an international park – protected by the UN. "I see their bulging eyes," says John Sauven, head of Greenpeace UK, of the international powers who are eyeing up the Arctic as a prize. "We've rampaged around the world's oceans and wreaked destruction in the rainforest. That endless plunder, increasing in velocity and intensity, is about to hit the North Pole. Originally viewed as an inhospitable wasteland and essentially valueless, now with the melting ice it is seen as a source of riches. Countries are lining up their military fleets to plunder it. This is the defining ecological battle of our time. The Arctic faces an incredibly dramatic situation."

Jarvis has been to the Arctic. "Not that I'm a massive expert, but when I heard that they wanted to dig it up, I thought: hold on a minute – that's not good," he says, in his undramatic way. Back in 2008 he joined a Cape Farewell expedition to Disko Bay, north of the Arctic Circle ("And we did have a disco, too, one night," he clarifies), with KT Tunstall and Marcus Brigstocke. Cape Farewell is a project created by artist David Buckland to set a cultural context for and response to climate change (it's the sort of concept that leaves climate-change deniers foaming at the mouth). The main idea is to set up a partnership between cultural and scientific institutions to improve the public's engagement with changes in the climate. Creatives who've got involved and visited areas affected by global warming include Jude Kelly, Yann Martel, Martha Wainwright, Ian McEwan and Gary Hume. It's hoped that the expedition will loosely influence their work, but it's not linear. "David doesn't go: 'Right. We've got you up here where you can't escape – write a song' or 'McEwan, I want 10 pages now,'" says Jarvis.

Atone point – the evening when their boat, the scientific research vessel the Grigory Mikheev, drifted through a steep ravine one evening – Jarvis had a moment. "I was up on the deck and I wanted to start crying. I can't say why – it was perhaps because there was a spectacular type of landscape, and also that thing when there's no sign of people – and that's how it should be. Now you might comment: 'Well, that's all right for you to say, because you went there and you saw it.' But the point was that there are these forces, like these glaciers moving rocks and stuff over millions of years, and that's a process going on and we really shouldn't be fucking around with that. We don't understand it."

I wonder if this epiphany has had an effect on his own behaviour. "Yes, I probably have changed a bit, actually." The cloth bag he carries may well be an indication and he's often to be seen on a bicycle around London. He favours the low-emission Eurostar – he is some sort of cultural ambassador for the train company and hops on it frequently to visit his son Albert in Paris. "But I don't want to be a zealot," he points out. "Ordinary people get blamed for too much. You have to accept that people want stuff. And you don't want to get into that thing in East Germany where everybody had to drive a Trabant. You can't remove all choice. Like, I don't think saying to people that you can't drive a car any more is going to work: you know in your own car you can put your music on right loud and pick your nose." I almost point out that's no preclusion to using the bus where I live, but he adds: "Generally, left to their own devices, people want to do the right thing."

You can't ever really imagine Jarvis becoming a preachy green. It will be interesting to see how he sits with this turbo-charged Greenpeace campaign, which will necessarily involve stark demands. If it takes Jarvis to its bosom, the eco movement will have to get used to more discursive activity. Jarvis is highly discursive. He thinks this may have been his problem when he appeared on Question Time in 2009. "I want to apologise for that – I wasn't very good on it," he says. Critics suggested he'd been too lazy in his QT preparation; actually, he says, the problem was that he just wasn't up for playing the usual adversarial game. "I got a feeling I was supposed to be in opposition to Peter Hitchens. So I was supposed to clash with him and get uppity every time he said something, but I ended up agreeing with a lot of it. And then I'd notice Dimbleby started twitching his eyebrows at me in a weird sort of eyebrow dance."

Are you sure, I ask. "Well yes, unless he's got a really bad twitch. So he was signalling at me to come in with the opposite opinion, and I just thought: 'No. Fuck off.' It's that thing that everybody thinks is great telly. Well, what would be great is if you have a discussion and at the end everyone agrees. For TV you also get those pre-interviews when researchers ask you what you're going to say. The pre-interview drives me insane. If they've already decided the outcome, why don't I just hand in an essay? Maybe if we talk we'll find something out. I'd rather just have an awkward pause." This is the way Jarvis conducts his own conversations on his 6 Music show Sunday Service.

Still, he is capable of taking a stand. He spoke up in favour of the Occupy movement and got in a bit of trouble for joining a student march against university- fee increases in 2011 and supporting the protests against tuition fees so vocally (not impartial enough for someone who works for the BBC, apparently). He opens up a marvellous opportunity for me to mention the unmentionable. Does he feel remorse for that stage invasion incident at the Brits in 1996 now that he's engaged with the Arctic and other environmental issues? After all, Michael Jackson was merely giving an epic performance of "Earth Song", presumably directing our attention to the strife of the planet. "Well, and pretending to be Christ," says Jarvis, only slightly rolling his eyes. "It is a right good song, obviously.

"Actually there's something I want to say about that and David Cameron," he continues. "I'd like to set the record straight." When the Guardian put selected questions to the prime minister in 2011 they included one from Jarvis: "Re: abstract finance ideas such as derivatives and futures, do you actually understand how all that stuff works? And if so, can you explain what a derivative and future are?" Having made a reasonable fist of explaining derivatives and futures, Cameron then "spoiled it for himself", according to Jarvis. In his sign-off, the prime minister says: "There we are. Not as punchy as Jarvis Cocker on Michael Jackson, but it's the best I can do. I was there that night, at the Brit awards. I saw him led away. I saw his bum."

"I'd just like to point out," says Jarvis, drawing himself up very straight in his chair, "that if anybody cares to look at the video evidence, at no point was my bare backside revealed. So therefore the fact he says he's seen it totally negates the credence of what he said in the previous part of the answer about derivatives and futures. I'm glad I've got that off my chest – it's been bothering me, that."

Not, you understand, that Jarvis wants us all to be squeaky clean and incapable of general rascality – a term coined by philosopher Alan Watts, of whom he's a fan. "The good thing about people really is their iffy-ness and dodginess, isn't it? Everybody is out for themselves, really, but that shouldn't mean that everything needs to get messed up. And if everything goes down the pan environmentally, then of course none of that could happen. We wouldn't have time for that inherent iffy-ness in a post-apocalyptic landscape, would we?"

This is eco logic, but not as we know it. So let me get this straight, Jarvis: you want to protect the earth to give shadiness the proper space it deserves? "Yes," he says, grinning from ear to ear. "I want to set up a haven for that."

If Jarvis seems more flippant than your usual eco warrior it's probably also a defence mechanism. Those with a high profile have to be prepared for some derision if they extol eco credentials while continuing to live a comfortable celebrity lifestyle. Even his Cape Farewell expedition, for which he did relatively little publicity at the time, caused one music critic to refer to him as the "Indie Sting". "I'm sure Sting's a lovely guy," he says, attempting the diplomatic approach. "It's just that nobody wants to be seen as that holier-than-thou thing. That over-earnestness is a bit of a problem with people in bands and celebrities or whatever. There is that irritating thing where people just try and give themselves a bit of extra gravitas, like: 'I'm not just in Transformers III – I'm saving the world!' I know it's irritating. All I can say is I feel a bit of a personal involvement in the Arctic because I've been to that part of the world."

According to Sauven at Greenpeace, its new campaign will require unprecedented global public support, and we will have less than three years to come together to avoid catastrophic ecosystem destruction. "If this campaign is successful," Sauven says, "it will be because people like Jarvis have lent their support and their ability to reach out. We urgently need this to happen globally." It raises the question: how far is Jarvis willing to go for the planet? Might Britpop's chronicler of contemporary life be one day remembered more for fighting off bulging-eyed Arctic plunderers than for "Common People"?

"What you mean – will I spend all my time on a boat?" He pauses to think. "Perhaps I'll be tied on the front of the ship. It's not going to be me or any one individual – it takes everybody for things to change. I'll try my best. I shall maybe go and buy some thermal underwear as a start.