On Venice Beach the surfers slip and slide through breakers glistening in the winter sun, of which there is plenty in this sybaritic corner of Los Angeles. Here Camden Market boho meets the last tattered camper vans of the hippy dream. The shabby-chic jumble of wholefood shops, piercing parlours and millionaire condos is one of the few communities round here unscathed by the Los Angelinos’ love of a six-lane freeway.

The latest to join the local cast of artists, dreamers, yuppies and bums is the singer-songwriter Melody Gardot who, instead of retreating to her home city of Philadelphia during breaks in a hectic touring schedule, finds her rest and recreation here. “I come to rejuvenate. It’s hot and I’m anonymous,” she says, stretching out on the sand. “You don’t have to worry about catching up or bumping into people. I’m like some old Persian princess — here’s a bed, here’s a palm tree and I’m happy to lie here for days.”

It’s been a helter-skelter year for Gardot, widely touted as the natural successor to Norah Jones and Madeleine Peyroux (though with rather more charisma than either). She’s played a blur of jazz festivals in Newport, Montreux, Rotterdam — and now London, thanks to the success of her debut album, the sultry jazz-blues of Worrisome Heart. Her two appearances next week will come almost exactly a year after the 23-year-old made her first foreign foray. “I played a little club in Piccadilly. Croatia had just beaten England. It was a horrible situation. Everyone was at the bar, depressed.”

Early in her career, she was also often in pain. “Sometimes I would forget the words, my back was hurting so bad.” To see Gardot today, a tanned, toned blonde, it’s hard to imagine the injuries to brain and body that nearly killed her. But at 19 she was knocked off her bike — and the long road to recovery inadvertently sparked her musical career.

Gardot famously began composing during the music therapy designed to reenergise her neural pathways — and the songs that would become Worrisome Heart poured out. She does, though, still wear dark glasses because of increased light sensitivity and carries a gold-tipped cane — “I say I’m anonymous, though I’m the only person under 70 walking round with a stick” — but she’s relaxed, upbeat and has a girlish impetuosity (after the interview, she insists on buying me a trilby from her favourite hatter).

Her success is so new that her impact on the world has not quite sunk in. She is delighted to get a text from a friend saying that her music’s being played at Boston airport. Recently she picked up a compilation CD called Women in Jazz at her wholefoods store. “I put it on the headphones to see who these women in jazz are and it’s me first track!” She smiles. “I just wanted to make a record that felt good. I was surprised when people lined up to buy it — and kept buying it.”

She has spent the year turning up in countries she had never visited before to find theatres full of people waiting to acclaim her. “Sometimes it can bring me to tears and I’m so grateful. But it’s heavy, too. I can only liken it to a situation where someone is in love with you but you’re not quite in love with them but you’re glad that they’re in love with you as much as they are. It’s overwhelming.”

She understands how performers can get hooked on the approbation of strangers. “It’s somewhat addictive — and most musicians have addictive personalities. So, when a tour ends, it’s hard.”

Not that Gardot’s schedule is the stuff of rock’n’roll excess. Because of the accident she tires easily and dates have to be carefully organised. Her tote bag contains a yoga mat, Pilates band, amber incense, instant miso soup and lavender oil. There’s raw honey in case of vocal problems, and if that fails a swig of cognac.

She regularly gives talks on music therapy. “It’s not that I’ve got a PhD but I went through the school of hard knocks.” She sometimes finds it hard to talk to medical professionals, “because I’ve done Western medicine and I’ve shifted East. The Western medicine might have temporarily quelled the problem but it did not solve anything for me long-term.”

She still does not understand how an interest in music — she used to play piano in bars — turned into an all-consuming passion during her recovery. “Before it was an intellectual interest, it was left-brain. Now it’s right-brain.” And the music keeps coming. She already has the tunes for her next album recorded. They are “more ambitious, more cinematic, and a little ironic sometimes.

“You don’t sit down consciously to write. It’s an itch, you tread over to your instrument and this gelatinous, liquid, amorphous energy surrounds you and suddenly you’re playing something and the melody, the lyrics, are there.”

Music-making and the effects it can have on listeners are a deep mystery to her. “It’s like the end of the tour, in LA. The night was just ready. There was like a haze in the room, a weird energy. We finished [the ballad] Love Me like a River Does and there were about 50 or 60 seconds of silence. It wasn’t because it was bad but people just didn’t want to clap, they didn’t want to break the spell. I looked at the bassist, the bassist looked at me, the drummer looked at me. It was like ‘What did we do?’ It’s almost dangerous — we took people to a space and kind of left them there, suspended.”

The new tunes, she says, are full of hope “from someone who is known for writing gloomy lyrics”. Does that mean her Worrisome Heart has found a kindred soul? She laughs. “Well, it’s not David Beckham or anyone that the papers need to print. I wouldn’t be able to write about love and heartache without having someone around. There’s always someone; there’s a reason why my heart continues to beat.”

If there is a cloud on the horizon it’s to do with the speed that her career is moving. “This year I’ve been to all the places I ever dreamt of going.” She laughs. “I’m a little nervous. They say that you die when you’ve nothing left to do — but I’ve done everything that I wanted to do. Am I going to croak in the middle of touring?”

Melody Gardot takes part in Jazz Voice — Celebrating a Century of Song at the Barbican, EC2 (www.barbican.org.uk), on Nov 14, and headlines at the Festival Hall, SE1 (www.southbankcentre.co.uk), on Nov 15 2008

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