Imagine a sensuous, languid cat with the sex appeal of Rihanna and the personality of a punk, and you will have a picture of Debbie Harry. Blondie's lead singer has lost none of her sultry dissidence that first captivated fans more than 40 years ago.

It's quite a relief for her to be in the UK, for back home in the US, Donald Trump dominates every conversation – 'You can't get away from it.' And to make matters worse, Debbie's own relatives are supporters of the new president.

'Sadly, yes. I come from a conservative family and that's a dreadful thing. It's horrible to know they are, and to not call them and scream at them. But,' she smiles with a shrug, 'I can't do that.' Debbie always knew she was a misfit, and escaped her small New Jersey town as soon as she turned 18.

'I knew I wanted to be some sort of artist, and I knew that if I had to stay, get married and have a family, I would have a nervous breakdown by the time I was 40.'

In Sixties New York she partied wildly, making friends with everyone from David Bowie to Andy Warhol and joining various bands before forming Blondie in 1974 at 29 years old with a guitarist who would become her boyfriend, Chris Stein.

Blending disco, punk, rock and pop, Blondie's 1978 album Parallel Lines made them global superstars. After hits with Heart Of Glass, Hanging On The Telephone, Call Me and One Way Or Another, Blondie broke up in 1982 and Debbie nursed Chris through a rare autoimmune disease before the couple also split up.

The band reformed in 1997, playing at festivals until releasing their comeback single in 1999, Maria, which went straight to number one. Having sold more than 40m albums*, they are now about to release their 11th, Pollinator, an irresistible record that sounds unmistakably like Blondie yet is so contemporary that hipsters from Brooklyn could have made it.

Debbie Harry - Blondiepinterest

Debbie puts the current sound down to collaborations with Sia, Johnny Marr, Charli XCX and others. 'It was a fresh approach for us to bring in so many outsiders,' says Debbie. 'And it's kind of perfect for the stage in our career to do that. One of the comments I hear from a lot of people my age is, "Oh, there's no good music these days." It's unfathomable to me how anybody could say that. There's so much great music.' She pauses to consider. 'People's lives change when they start having families, I guess. They're not going to experiment so much.'

As for Blondie, by contrast: 'Maybe we all have delayed adolescence or something,' she grins. Debbie and Chris remain close friends. 'My partnership with him has been, you know, a phenomenal, wonderful experience that's lasted my entire adult life. For some reason, it's just held up. I don't know why, exactly, but it was a true meeting of the minds.' He's married and has two daughters – to whom Debbie is godmother – but she never wanted to start a family and settle down. She is great friends with the performance artist Marina Abramović: 'And you know, she says the very same thing – that she never contemplated raising a family.

It's always been a personal search, or a quest, dedicated to art.' To her teenage self, it would have been unimaginable for a woman to still be making music in her seventies, but it seems perfectly natural to her now: 'I'm not a sociologist, but women's roles have changed and [my career is] totally correspondent to that. We're the lucky ones, you know, to have a sort of break in that bondage.' Debbie lives alone in Chelsea, New York, and likes it that way.

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She laments the city's gentrification – she can't stand the preppy way the wealthy all dress the same, 'in that dreadful uniform', and finds the tourists a bore – but she can't imagine living anywhere else. People often assume she is fabulously wealthy herself, but in fact Blondie signed a disastrous record deal in the Seventies. 'It sucked. It really was very bad. We didn't make any money for a long time.' Does she still need to make money? 'I like to make money,' she grins. 'I really like to make money.' She has always been a feminist, because 'I wanted my freedom, and freedom of choice. I was kind of stubborn.

'I could never understand why guys got to do everything.' She wasn't always fearless, though. 'I had to overcome fear, you know. I didn't like having it but, as I say, I was really, really stubborn and determined. I mean, when I left home I guess I was terrified. You know, what on earth would I do? God, I had no wherewithal. I just knew I wasn't happy, and I wanted to be happy. And I was drawn to an underground culture…' She breaks off abruptly. 'Let's not dwell too much on the past. Let's talk about the future.'

I wanted my freedom, and freedom of choice. I was kind of stubborn.

I'm curious to know how far Debbie's private, domestic self differs from her public persona, but she looks puzzled by the question – 'I don't know. I'm just me' – suggesting the answer is: very little. She doesn't buy much music these days, and isn't even sure if she has a Spotify account, but likes to listen to cable radio in the car and watch new bands on YouTube.

Her fascination with fashion has only deepened over the years. 'I just love it. I don't know if it means I'm a girly girl or what, but it is definitely an art form.' She is currently working on her own clothing line, which will be 'a very, very street vibe kind of thing. It's based on urban camouflage, very wearable and comfortable.' She does date, but only men these days. 'My bisexual days have gone by, actually. I have great affection for some of my female friends, but I think maybe whenI was younger it might have been a little bit more hormonal, and our hormones change.' She's not surprised that 50% of millennials say they're not 100% heterosexual**. 'They're exploring all the options, and perhaps that's what I was doing. It just seems that now we can deal with it a little bit better, for some reason.'

I could never understand why guys got to do everything

Debbie is so magnificently insouciant that I wonder what she makes of her status as an icon of pop. 'The first time I heard [that phrase] was in the Nineties, and I was sort of horrified. All I could think of was, you know, a religious figure or something. And, oh God, I can't bear that.' Gradually, she came to see what people meant by it, 'but I don't know if I believe that's a good word for it. I think I like the idea of being a star, a superstar or a pop star. It seems more in keeping with your real, relative value. Icon is like, you need to die first, right? You should be dead and then you can become an icon.' She laughs, a gravelly purr of defiance. 'And I'm not dead yet.'

Blondie's new album, Pollinator, is released with BMG on 5 May