Interview: Julian Casablancas, singer, The Strokes

THE man who wrote, sang and wore the Converse on what many consider to be the greatest rock album of the Noughties is two and a quarter hours late. That's not rock star late, it's supermodel late – which, given Julian Casablancas's back-story, maybe isn't all that surprising.

John, the father of The Strokes' frontman, founded the Elite model agency in New York. Strictly speaking, Cindy Crawford wasn't Julian's babysitter and Linda Evangelista didn't pop a toy Maserati in his Christmas stocking. Nevertheless, the connection to the world of impossible beauty and dreadful time-keeping has been just another reason for the cynics to sneer – on top of Casablancas's own good looks, privilege, posh education and the apparent lack of setback or even sweat in The Strokes' effortless ascendancy. So, when his band lost their way and he became a party-pooping drunk, the reaction was: "That's too bad."

But Casablancas, now 31, is ending the decade as he began it: on a tremendous high. The Strokes' 2001 debut album Is This It, which made indie guitar rock sexy again (and obliged short, round men of unStrokesian litheness to squeeze into drainpipe jeans), has been voted the decade's best by the NME. Now he's finally released a solo record and Phrazes for the Young has been greeted with surprise and acclaim.

Casablancas is backstage in Rotterdam where – en route to Glasgow this weekend – he is playing a festival called Bazar Curieux, which would be a useful description of his album's mix of wonky synthesisers, New York history lesson and drinking confessional. The venue, the Maassilo, is a supertrendy waterfront club fashioned out of a former grain warehouse where it would be easy to lose a skinny, elusive rock god such as Casablancas, but his only explanation for his tardiness is that he'd been "taking a shower".

Never mind, he's here now, smiley and eager, and I have three questions for him. How much, since exiling himself in Los Angeles, is he missing New York? How much, since cleaning up, is he missing the booze? And how much is he missing The Strokes? He takes the easy one first. "Well, I didn't end up staying in LA. I loved it there, the perfect weather, but part of the reason was I always knew it would be temporary. New York is in my soul." It's also the city where his first child, with his wife, Juliet, will be born, due early next year.

What kind of dad does he reckon he'll be? "I'm kinda thinking: Best Dad in the World!" What did his mother and father teach him about parenting? "Uh, how not to do it? I'm joking, kind of. I'm just going to try and be a good dad and not spoil the kid: give him love and encouragement but also discipline. Me and my woman, we don't want him to feel too entitled."

Casablancas's upbringing always comes up in interviews. Correction: he says it always comes up in British interviews because we're more fascinated than his homeland in his elite schooling in Switzerland. He seems to have a point – UK album reviews are still namechecking the Belgian and Luxembourgian royalty with whom he shares an alma mater. The last time the issue cropped up in a UK newspaper he accused the journalist of being "borderline insulting", but he's relaxed about it today.

"It's gotten exaggerated," he says. "Some of you guys think of me in a V-neck tennis-club sweater, driving a Bentley, but my teenage years weren't like Gossip Girl. I went to that Swiss school because my dad had gone there before me but I only stayed for 18 months."

Casablancas's fashionista father had an affair with the model Stephanie Seymour when she was 16; his mother is Jeanette Christiansen, herself a former model and Miss Denmark. "I was brought up by my mum, but obviously the times I saw my dad I got glimpses of his world, which was insanely glamorous. At that school, though, I was probably the only kid who didn't have a trust fund. I hated the vibe; this idea that just being there would be enough in itself to have all these doors open for you."

Casablancas started drinking before his teens and had to be enrolled in an after-school club that was a form of rehab. He refuses to blame his habit on his parents' break-up, praising the positive influence of his stepfather, Sam Adoquei. Mostly, he loved booze. On his solo album, the song Ludlow Street begins: "Everything seems to go wrong when I start drinking." When it began to affect his music "and other things," he had to quit.

He says he can't wait to get back to Glasgow, scene of many epic Strokes gigs where a tough crowd would traditionally give the support act a torrid time ("They threw beer and stuff which probably wasn't beer") before his band even took the stage and, if they were lucky, the show would turn into "this symbiotic, awesome, beautiful thing". And afterwards he always wanted to drink. A lot.

"I was a monster," he says. "When I was younger I thought it was cool to drink ten times more than everyone else. In The Strokes I was drinking to the limit of messing up my life; if I wasn't drinking I'd actually be in physical pain. Pounding down a bottle of vodka a day and all these shots of Wild Turkey seemed great to me; it wasn't for everyone else. As far as I was concerned I was the best pool player in the world, telling the best jokes in the world. But after 43 minutes you only think you're the coolest person; actually you're an idiot.

"I drank my life's worth of alcohol in a ten-year span, then had a hangover that lasted three years. I miss drinking every day but I can't just have one glass of wine, so I've blown it. I've got lots of beer on the rider for this tour and I'm having to watch my band have a good time while I sip soda water. But don't feel too sorry for me because right now I'm happier than I've ever been."

So, final question: whither The Strokes now that four of the five members have released solo records, with Casablancas – always the band's main writer – proving on Phrazes for the Young that he may no longer need his old prep-school buddies? It turns out to be the trickiest question to answer. Of the chances of a new band album in 2010 he ums and ahs for a long time before saying: "Sssssixty four … and a half per cent."

He didn't want a solo career and says he felt pushed into making his own record after the others did their own things. "I really dig people are remembering our first album and it's figuring in these best-of-decade polls, but sadly that's not going to get us back into the studio." So what does he give the rest of The Strokes for Christmas? "This year, maybe nothing. Or is that bad? I have a gift bin where I randomly chuck stuff throughout the year so maybe I can find them some posters or something … "

Julian Casablancas plays the ABC, Glasgow, on Saturday.