If you paid close attention to Live Earth last month you may just have spotted, squeezed on to the Wembley bill somewhere amid Madonna’s theatrics, Metallica’s heavy metal and Ricky Gervais’s bad gags, a young woman called Terra Naomi. Armed only with a guitar and a nervous smile, the American singer took to the stage to perform one song, Say it’s Possible, at the personal invitation of Al Gore, her lyrics having been inspired by his film about eco-apocalypse. The tune had already been a huge hit on YouTube, clocking up five million views, but she was still an unknown compared with the other artists. Yet nobody in the Wembley audience was as amazed to see her there as her dad.

Her father, a plastic surgeon, had flown over from the US with her brothers especially, unable quite to believe this was the same daughter whom he had dragged from the crack houses of Detroit into rehab. What’s even stranger is that she became a drug addict while training as an opera singer at a music college in Michigan. By day she was learning Britten arias; by night, she was “a dealer and a junkie, sticking needles into my arms 15 times”, as she puts it.

Sitting in a pub near the Brighton church venue where she will perform that night, Naomi relates such stories breezily – though she is obviously horrified by her own past. Naomi is strangely cute, and time passes quickly in her company.

“Someone at my record label was talking about crazy rock’n’roll behaviour the other day, and I was like: ‘I was doing that s*** when I was singing opera; that’s rock’n’roll man!’ Everyone in the crack houses was high and I’d sing for these prostitutes. They’d be like: ‘What did you do today?’ and I’d say: ‘I sang in an opera’, and they’d say: ‘What’s opera?’ So I would just start singing.” She laughs and curls her skinny limbs around herself. “I think I gave them some very bad dreams.” After her turnaround, Naomi is now a fully fledged rock-pop singer and about to release her debut album, Under the Influence, through Island, home of Amy Winehouse. She sees something of her younger self in her labelmate, and recalls attending a Winehouse gig “with the head of our label and his wife, sitting up in this little VIP section, and Amy’s whole family was there. I’m really close to my dad and I guess it really hit me because of what I’d been through, and because we are both daddy’s girls. Knowing that my dad was the one who watched me on stage but also the one who picked me up off the floor and put me in the car and drove me to detox. She did put on a good show, but she looked like she was having problems, and seeing her dad have to watch that ... It was just sad, really sad.”

Not that Naomi has much truck with the celebrity rehab craze, having done hers the hard way. She is concerned that luxury rest homes for “exhausted” celebrities do nobody any good. “When I went it was to an emergency detox hospital for crackheads in upstate New York, because my body was so ruined, and then rehab was a month on a hospital wing – I think I was the only one who wasn’t court-ordered to be there. The other women were really f***ed: ten kids, no teeth, the lowest of the low. They made me scrub toilets and I know they’re not doing that in the Priory; they’re riding horses and having massage. I think that’s why rehab worked for me – it was so disgusting that, my God, the thought of going back. . .

“I was using drugs in the ghetto of Detroit and there was nothing cool about it. There were guns. The situations I was in were life-threatening.” How she got into such a state she isn’t sure, as she claims she had a decent childhood with a nice middle-class family. She just always felt like an outsider, the sort of kid who hung out on their own wearing black and writing morose poetry, and her determined streak led her to wanton self-destruction. Even when studying opera, she made friends with people in rock bands, and so after quitting the drugs she also quit opera. “I knew classical music wasn’t really for me – I didn’t have the discipline or the love.”

Her music now is much more like that of Alanis Morissette, with first-person confessional lyrics. Though it sounds commercial on record, live, it is clear why she has been booked as a support act for the idiosyncratic Martha Wainwright. They both have rich, soaring voices and a deep well of life material on which to draw.

At the Live Earth gig, Naomi was even more determined to enjoy every second on stage, as the drugs had made her so numb for so many years. “So I thought, I really want to know what it’s like to stand in a stadium singing in front of 75,000 people and then millions more on TV. It was completely overwhelming and surreal at the same time. I still don’t really believe that it happened.” The month before she had been playing to 100 people in Camden.

Such is the power of Al Gore’s personal support. She saw An Inconvenient Truth while she was working as a bored waitress in New York. “The next day I wrote the song that I recorded and posted online. Somebody at YouTube loved it and put it on the front page. That was in June and by August I had all these people calling me and wanting to sign me. I was like, what is happening here? It was years and years of no interest and then all of a sudden it wasboom, switch, everything’s changed.”

Gore got involved after Naomi spotted him at a Grammy party. “My friend said, ‘Look, there’s Al Gore’, and I said ‘Ooh I have to talk to him to tell him about my song.’ It had already changed my life . . .” It was to do so all over again.

Terra Naomi’s single Not Sorry is released on Monday. The album Under the Influence is out on Sept 17, both on Island

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