Debbie Harry's still rocking

I'm at Hakkasan in Mayfair, in a state of extreme anxiety. It's not only that — girl crush! — Debbie Harry was the first pop star I ever liked. Nor is it that, hearing her on Desert Island Discs the other morning, she sounded just a touch tricky. No, what it really comes down to is this: While she continues, at 65, to be one of the coolest women on the planet, I remain, at 41, one of the squarest.

She arrives about 20 minutes late — a vision in black Lycra (or something else quite stretchy) and big sunglasses. But I like her immediately. She is kind. She exudes good manners and a certain kind of professionalism, and takes it in her stride when, even as she is still perusing her menu, I blurt out what must surely be the daftest question she has ever been asked. So, I say, what did you eat when you were a punk? "What did I eat when I was a punk?" The briefest pause. "Well, practically nothing. We were broke. We used to go to Chris's mother's house [Chris Stein, Blondie's guitarist and her ex-boyfriend] and have this kosher beef dish she made with lots of garlic in it. We went to Chinatown for dumplings. We used to have canned chilli. I would make baked yams, which were healthy and economical. I can cook; not great, but I can. I like cooking for other people but I don't for myself. I mean, why bother?"

We're sitting side by side at a tiny corner table, which means that I am able to examine Harry's face minutely. She looks amazing: peachy is the word. A lot better than she did ten years ago. "I was in a slumpy kind of period then, and I'm not now. I'm on a big regime because I want to feel my best. I have a trainer. He's a monster, but I love him."

She had a facelift in the early 1990s, a fact she has never tried to hide. Would she still have had a facelift if she hadn't been a pop star? "Yeah. I think if I'd been very depressed about myself, I might not have done it. But it gave me encouragement and satisfaction." Of course ageing makes her anxious. Am I kidding? "Everyone, at some point, has a realisation about their longevity, or lack of. How you respond depends on how much you like living. I think for men, the ageing process is more evenly paced. But for women, all of a sudden, a page is turned. It really is radical and hormonal. Women just have a more rigorous time physically than men. It's a challenge."

Did she expect to be touring in her sixties? No, not for a minute. "I did those solo albums at the end of the Eighties, and they didn't do very well, and I had no inclination to do Blondie again [the band split up in the early Eighties and did not reform until 1997]. I like performing, so I probably would have figured out some kind of smaller act, a cabaret thing." She belongs, she readily admits, to the first generation of ageing rock and pop stars, though in her view 70 is the new 50. How will she know when to stop? "I guess when there's no longer an audience. But I've gone this far ..." From deep inside her there comes a croaky kind of laugh.

I love it that Harry isn't a moaner. "Fame is important so far as having an audience goes, and enduring and stuff like that. How else would you do it? So you don't complain about it." But most famous people do. They complain about being followed by their fans. She shoots me a look. "Well, you can always tell them to stay away. No, I appreciate my fans. How would I exist without them? If I'm out without make-up and stuff and not ready to be photographed, I just say: ‘No.'" Wow. Quite sane. "Well, I suppose I have a bit more anonymity than Madonna, or Gaga. They're super up-there. I'm more of a cult figure."

Her parents wanted her to marry and have a family, though this never happened; in the 1980s she nursed Stein through a serious illness but then they split up, and she is now godmother to his children with someone else. The rock chick daughter was the last thing her parents expected. "I was very shy and quiet, and all my ambitions were dreams. I hadn't a clue about the music business: just this drive, this obsession, that I can't explain."

Is it lonely, life on the road? I hope she has someone waiting for her in New York. "No, not particularly. I date. I don't love dating but I hope to do it more; I wouldn't say ‘no' to one wonderful relationship." Do men find her intimidating? "I suppose some do. But that's their problem." Is she a feminist? "How can one be a woman and not be a feminist? That's my question."

I'm calmer now. Debbie has created the soothing illusion that we are bonding; she even tells me that my questions are, well, if not exactly interesting, a nice change from all the music stuff. But then her PR appears and I well and truly fluff it. As we wait for our waiter, Harry asks me if I like cooking. Yes, I say, very much. I reach into my bag, pull out my phone and proceed to show her a photograph I took of the salad I made last night. "Oh," says Harry in her light, rather distant voice. "Oh. That's beautiful." She hands my mobile back to me. Then she turns to her PR. "Please make sure Rachel gets tickets to see us," she says. She smiles at me, then she gathers herself and leaves.

I can hardly believe it. I had lunch with Debbie Harry, and what did I do? I showed her a photograph of ... a salad.