The Maldives is a cluster of 1200 coral islands sprinkled across the Indian Ocean. Viewed from an aerial height, they look like droplets of pearlescent petrol on water. For decades, this nation has been synonymous with 'paradise': the ultimate luxury destination for the world's wealthy, for holidaymakers and honeymooners. But a few years ago, it began to disappear from the travel supplements of Sunday papers and appear instead on the broadsheets' back pages. In 2008, Maumoon Abdul Gayoom, who had ruled the country as a dictatorship for 30 years, was replaced - in the country's first democratic election - by Mohamed Nasheed, a human rights activist who had been imprisoned and tortured under his predecessor's regime. A year later, at the 2009 climate summit in Copenhagen, Nasheed again made the news with his desperate plea to other world leaders to commit to reducing carbon dioxide emissions. Rising, on average, only 1.5 metres above sea level, the Maldives are currently being destroyed by global warming; swathes of coastline are swept away into the ocean every day.

The Island President, which has won acclaim at the Sundance, Telluride and Toronto film festivals, follows the eponymous leader – a spritely, smiley David – as he battles to fight off the three-headed Goliath of dictatorship, climate change and global indifference. The documentary tells a feel-good story of triumph-over-adversity, undercut by an almost unbearable sense of doom. At one point, the usually irrepressibly optimistic Nasheed, ashen-faced and exhausted by the endless squabbling between nations at Copenhagen, exasperatedly asks: "Why are we arguing about these things when we're all going to die?" The soundtrack feeds the sense of impending disaster. Radiohead, purveyors of what the director describes as a "neurotic sense of awe", have spoken out in support of Nasheed's cause and provided 14 back catalogue songs for the soundtrack, bringing it further pre-release publicity.

In February, after the cameras had left, Nasheed conceded power to the opposition, following controversy caused by the arrest of Judge Abdulla Mohamed. Nasheed later described what had happened as a coup. A few weeks later, I talked to The Island President director Jon Shenk.

When did the political and environmental plight of the Maldives first come to your attention?

Jon Shenk: The story made what you might call minor international news. And the reason it did was that prior to the Arab Spring of 2011 it was actually quite unusual that a nation that had been ruled by an autocrat dictator for 30 years - and which was also 100 per cent Muslim - had essentially just elected its first democratically elected president. When Nasheed came in, he'd already been working for most of his life for the cause of democracy. And then he stepped into office and immediately began to make quite dramatic statements about the environment - that his people needed a new homeland because their islands were sinking. I read about these things and I just thought, this is amazing - this combination of details.

What made you think that all of this would make a good subject for a documentary?

JS: I really made the film because Nasheed is such an incredible person - with so much charisma - and because there's such inherent drama in what he's trying to do, both domestically and internationally. And here's the thing: climate change and global warming elicit yawns in people these days, and when I read about Nasheed I thought it was kind of chilling. Here we are, there's an impending apocalypse for Planet Earth, and people are unwilling to deal with it. And from a storytelling perspective, here comes a hero who can potentially save the world.

All of this combined with the fact that we were going to get access to politics at a level that no other filmmakers had ever had. I just thought it was such an incredible opportunity to make a really dramatic film. And in terms of bringing to light what was going on in the Maldives, obviously it deserves attention, but I think that it's a story that's bigger than this. It's about a hero's journey: someone who's had to see clearly what injustice is and who has gone about trying to fight against that, using every means he has.

It seems that you could have made two films: one about Nasheed's coming to power, and one about the subsequent struggle against climate change. How did you choose which particular detail to focus on?

JS: We went into the film knowing that the plot would be primarily about climate change. But once we got into it, we realised that it would be impossible to tell this story without also relating the back story to people. In a sense, the first 'act' of the film is really about Nasheed's character: what motivates him, where he comes from, what his history is, his willingness to stand up to authority. In the editing – and even in the shooting - we really came to see that the struggle for democracy and civil rights in the Maldives is one and the same with the struggle against climate change. They are both fights for human rights, in one way or another.

You talk about the drama in Nasheed's story and when watching the film, it almost feels like it's too good to be true – a perfect Hollywood arc. Did you find that his story already fit this mould or did you, as a storyteller, have to mould it yourself?

JS: Obviously, Nasheed is very charismatic, very magnetic – he's one of those people who kind of jumps off the screen. And he was going through such a dramatic period in his life. He was the president, in power for the first time and he was travelling around the world meeting with international power-brokers. There's inherent drama in that. And then what happened in Copenhagen... we could not have predicted that he'd play such a central part in the negotiations. So in some ways it was just a series of many, many happy accidents for the storyteller. On the other hand, linking politics and climate change and making those things dramatic and engaging for the viewer was constantly on our minds. We were constantly pushing ourselves to keep it personal, keep it real, to make it visual and not scientific, and very human.

The Island President includes a lot of behind the scenes footage of the president in cabinet meetings, with his family, putting a tie on in his hotel room. How did you manage to get such extraordinary access?

JS: We told Nasheed, "In order for the audience to care about your issues and to care about your story they really need to see you as a man, and as a person, and because of that we're going to want to follow you into your strategy meetings and your cabinet meetings and your family life." And he said, "OK, yeah let's do it." In fact, later on he told me, "I really thought you guys would go away after a couple of interviews!" There have been documentaries that have been made about artists and musicians and everyday people, but it's very unusual for cameras to go into the kinds of places we go in the film, and for good reason – there are very sensitive things being discussed. Nasheed knew in his heart the power of transparency, the power of good journalism. And so I think in some way he saw us as kindred spirits. And at the same time, we just fought like cats and dogs to get in and see what we could. We pushed the boundaries of what was possible and there's no real secret – we were just really persistent.

Last month Nasheed was forced to concede power to the political opposition, in what he later claimed was a coup. What do you make of these most recent events in the Maldives?

JS: I think it's a shame. I think that Nasheed, by his own description, is trying to do an almost impossible task: to bring democracy to a country that's been run by an autocrat and a dictator for 30 years, a man who showed no problems with lining the pockets of his friends and giving government contracts to pay people off and that kind of thing. And when Nasheed took office there was a lot of momentum working against him. And I think, in a way, the film is all the more precious now because it shows Nasheed during a very unusual period in his life. He stepped off the streets and into the presidency and it shows what he was able to do in a really short period of time. I wouldn't be surprised if one day Nasheed returned to office... maybe, maybe not... but the Maldivians have tasted freedom now and, in a way, once somebody's had that, it's very difficult to take it away.

You mentioned earlier that the shift from dictatorship to democracy in the Maldives preceded the similar shifts in the Middle East. Do you think that the Arab Spring might have an effect on what happens in the Maldives?

JS: In a way, I think the opposite is true. The people of the Middle East have a lot to learn from the Maldives in the sense that the Maldives is a kind of harbinger of the pitfalls that exist once you really get into governing.

Do you feel that it's the responsibility of a documentary maker to bring important issues to people's attention?

JS: Absolutely. We're living in a time where there's fewer and fewer dollars in investigative journalism and I think in some ways documentary films have had to come into their own renaissance because of this. Because the world's hungry for stories that people haven't yet heard. But I think that of course the best documentaries are the ones which are great movies – ones where you just feel swept up in their beauty and their emotion and that 'take me away' kind of feeling. So I feel that documentaries first of all have to be emotional, have to move people - they have to be a movie - and secondly they have to ultimately make you see the world from a new perspective.

Could you talk about the soundtrack to the film? How did Radiohead become involved with the project?

JS: I'm a big Radiohead fan and from the very beginning - when I first saw the Maldives, looking down at those islands from the plane - I thought, If there's any way to capture that otherworldly, dreamlike, kind of neurotic sense of awe... Radiohead just captures that beautifully. And it turned out that Thom Yorke is actually very, very passionate about environmental issues and that one of the things he actually will speak up about is the environment. And through a friend of a friend of a friend we were able to contact the band and pitch them the idea. They already knew about Nasheed, and one step at a time we moved towards trying the music out and they really liked the idea. And they were so generous. The film takes on a completely new texture because of their music, and we're so grateful. For me, it was a dream come true: that this very unusual, very surprising story was helped by this exquisite, emotional soundtrack.

On film, the Maldives do look 'otherworldly'. How did you feel when you were there?

JS: It seems almost impossible that it can exist on our planet. And half a second after this thought goes through your brain, the next thing to go through your mind is, Oh my gosh, it's so fragile, so vulnerable, so precious. It almost seems like an accident of nature that it's there in the first place. And because of that, there's an inbuilt sense of vulnerability about the place. I felt fortunate that I had this opportunity to spend time there and at the same time I felt like, these islands, they are the canaries in the coal mines. And I thought what better symbol to show people: this is the kind of thing that will happen. It's just the beginning of potential disaster. And we need to work together to keep this from happening.

Ultimately, what do you hope The Island President will achieve?

JS: I hope that when people get to know Nasheed's story and see his passion and his really open, honest leadership... I hope that when some people see that they think, 'Gosh, I wish he were my president.' I don't know what it's like in the UK, but in the US, for some time we've been disappointed in our leadership. [We want] for leaders to lead from their sense of justice and from what they believe in, rather than from the polls. I think that Nasheed is one of those people that leads from conviction and I think that people need an example of that – those kind of crystal clear views that The Island President shows – I think that could be a really important thing.

The Island President opens nationwide this Friday March 30. A DVD release will follow on August 20 via Dogwoof.