Sienna Miller has never had a terribly comfortable relationship with her own fame. While she would like us to think of her as the actress who turned in a critically acclaimed performance as Edie Sedgwick in Factory Girl and stepped in at a moment’s notice to replace Helen McCrory as Rosalind in As You Like It in the West End, most of the tabloid-reading public know her as Miller Lite.

She is the rumoured wrecker of P Diddy’s relationship, the fiancée that Jude Law cheated on with his children’s nanny, the inspiration for the super-fashionable boho-chic and the dizzy blonde-about-town who goes to parties wearing knickers over her tights.

Today, though, Sienna hopes to harness her global celebrity to a more productive end. Only she seems to be finding the task a somewhat stressful one.

Sitting in her room at the luxurious Taj Lands End hotel in Mumbai, clad in slogan T-shirt and jeans from her own fashion label, she is exhausted not just from her jet lag but also from depression at the state of the planet.

Sienna has just returned from touring the Bandra Kurla slum, in which 350,000 people live in squalor on the banks of the sewage-infested Mithi River. “I’m feeling a bit shell-shocked,” she confesses. “It was unbelievable to see poverty on that scale, especially as it was combined with such a sense of togetherness. There were all these children running around, giving us hugs and asking our names.”

She is here as an ambassador for Global Cool, the climate change campaign. It has been launched in the country that is likely to feel the impact of global warming before anywhere else – even though its low-tech citizens are responsible for only a tiny proportion of carbon dioxide emissions.

In a diary of her visit, which she has been keeping for The Sunday Times, she writes: “Should the water levels rise due to global warming, the entire slum population of the city, an estimated 10m, will be left with nowhere to live. Bear in mind that the population of London is around 7m. It is vulnerable people like these who will initially be the most affected – unjust when you consider that the majority of damage inflicted on the planet had been caused by our lifestyles in the West.”

“What’s scary is that the river flooded two years ago and if it floods again the entire slum will be submerged,” she says now. “God forbid, because the water is ridden with disease and filth. Now I’m back here in the hotel with the air-conditioning and the elevators and the room service, I’m feeling completely sick.”

An announcement that she has adopted at least one slum infant seems inevitable: Hollywood A-listers seem to collect babies like the rest of us do Nectar points. “I think adoption is fantastic, but I don’t think I’m really capable of looking after myself as well as a child,” she says sensibly. In fact, she’s not even sure whether she wants to have children: “I’ve always aspired to have a family but I’d be nervous of bringing children into a world we’re destroying.”

For the past week Sienna has been hanging out with Bollywood big hitters Salman Khan (Bollywood’s answer to Sylvester Stallone, she says) and Amitabh Bachchan (“people here have been known to faint in the street when they see him”), hoping to get the message across to ordinary citizens.

She has also starred in a spoof film trailer along with Bachchan, Heather Graham and Tony Blair, the former prime minister, all posing as superheroes saving the planet by switching to low-energy light bulbs and sharing cars. “I didn’t meet Blair,” Sienna says rather grimly, “which is probably lucky. I’d have had a few things to say to him.”

The trailer was shown at the Bollywood Oscars in June and reached more than 400m homes on the Indian subcontinent. The attractively simple idea behind the initiative is to persuade one billion of us to commit to making small changes by, for example, unplugging mobile phone chargers or turning thermostats down a degree, so we can each reduce our personal carbon dioxide output by a ton every year for the next decade.

The theory is that this annual billion-ton reduction in emissions should slow the rate of global warming sufficiently to buy industry time to come up with sustainable energy solutions.

“It puts people at the heart of the solution,” says Julian Knight, Global Cool’s chairman and chief executive, who is with Sienna. “It’s not about being perfect, it’s about cutting down.” Cynics will doubtless suggest that it is also the perfect green-wash compromise for a Hollywood star who spends her life belching out carbon dioxide by flying around the world (Sienna returns to the UK tonight, flies to New York on Tuesday and then heads on to Los Angeles) but manages to feel less guilty about it if she switches her telly off at the plug before she does so.

“I have to travel – last week I was in five countries. It’s unavoidable. But I offset every flight I take and that helps,” she says.

And it would be unfair to assume that Sienna’s role as an ambassador is merely an eco-trip. She is committed to the environmental cause and has been for a long time.

Her arty parents believed in recycling decades before it became fashionable; her fashion designer sister Savannah, with whom she has just started up a carbon-neutral clothes label, twenty8twelve, is married to an eco-builder.

As for Sienna herself, she used to drag Law off on camping trips when they were going out and, according to one fellow camper at the time, vowed to do her bit to destroy genetically modified crops.

“I’ve always lived a green life in some degree,” she says. “I’ve always cared about the environment, I don’t drive a car, I eat organic wherever possible, I supported People Tree, the green clothing company.” She also voted Green “even though people said it was a wasted vote. But the more people say it’s a wasted vote, the more of a wasted vote it is,” she says crisply.

The sheer scale of the climate change crisis, however, left her, like most eco-worriers, feeling paralysed.

“I watched the documentaries; images like that polar bear floating on the melting ice cap stayed with me,” she says. “Then I’d go to parties and see how much energy was being expended just on entertaining us. I felt guilty and responsible, but also helpless, and I wanted to get involved but I didn’t know how. It felt like such a desperate task.”

So when she was approached by the charity in February to promote its user-friendly everything-makes-a-difference philosophy she accepted immediately – although the trip had to be rearranged when she won a role. “We were supposed to come in April, but I got The Edge of Love with Keira Knightley so they very kindly rearranged it.

“I take full responsibility for bringing everyone here during the monsoon, although we’ve actually been quite lucky with the weather, there hasn’t been too much rain,” she chats on blithely, before she realises that this may be a sign of the global warming she hopes to combat.

Her diary is more circumspect: “Everyone said we were crazy coming here in the monsoon season but it has rained only twice, making it one of the driest Julys on record. India is totally reliant upon the monsoon which feeds the entire country’s agricultural system. So we are witnessing the devastating effects of global warming first hand.”

At home in north London she says that she has taken the eco-philosophy to heart: her house is on a renewable energy tariff, she has installed low-energy light bulbs, switches off her appliances before she goes to bed, fills her kettle a cup at a time and takes showers instead of baths. “But I do have the occasional bath, too, to be honest,” she says guiltily.

It isn’t so much Sienna’s baths that are hastening climate change, more the energy-guzzling industry that employs her. Wouldn’t it be a lot easier to cut down on her carbon emissions by just giving up acting and the constant shuttle between London and LA?

“That’s my job and my passion,” she says. “I’m not going back and chucking it all away. And there’s a big community in Hollywood that’s very aware of the problem, what with Al Gore and Leonardo DiCaprio and the work they’re doing. A lot of films are becoming carbon neutral.” She has also persuaded her agency in LA to go carbon neutral, she says. “But I’m not a martyr, I’m not perfect and I’m not going to judge other people. You won’t find me hammering on their big trailer doors,” she adds with a sudden giggle.

Even if Hollywood were to turn completely green, however, I suspect it would still seem shallow and frivolous now that she has been faced with the grim realities of life in the slums.

“I feel completely crap about myself when I see how most of the world is living,” she agrees. “We’re spoilt and very lucky. But entertainment brings a lot of joy to people’s lives. There’s a level of superficiality to it but it makes people happy.”

There are limits, however, to Sienna’s desire to make others happy with superficiality. She says angrily that the level of tabloid interest in her is “really unfair” and consequently she has no interest whatsoever in confirming reports that she has split up from her musician boyfriend Jamie Burke over her friendship with P Diddy (or, alternatively, her Edge of Love co-star Matthew Rhys, depending on which gossip website you read).

“I’m not really interested in talking about my personal life,” she says uncomfortably. “I’m incredibly busy working right now.”

Professionally, it is true that she has never been more in demand with three films – Interview, Camille and Stardust – set for release this year and a further four in the pipeline.

Even with that body of work behind her she will probably still be for ever labelled Law’s party-loving ex – unless, of course, she can make a bigger name for herself as a green campaigner.

“Being called a party girl makes me angry,” she says. “My friends and colleagues know that’s not who I am, but in the meantime I’m going to try and do stuff that has meaning.”

She has already agreed to go to Latin America on the next stage of the consciousness-raising tour. “I’m quite keen to see Brazil,” she says.

“Hopefully I will be going on lots more trips. I’d like to rebalance my work, to do more of this sort of thing as well as filming. That doesn’t feel so important to me, suddenly. But then it never really did.”

Sign up today and find tips on how to help cool the world and save the planet at www.globalcool.org/myco2

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