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It must be pretty annoying when somebody else remakes your art and is much more successful than you. Who now remembers the original of Nothing Compares 2 U, when that video of Sinéad O’Connor’s extraordinary singing shaved head is etched in your mind for ever? Who can imagine Tainted Love without Soft Cell behind it? And as for It Must Be Love, well, it must be Madness, except it wasn’t always. And while the voice of Amy Winehouse can be heard belting out her hugely catchy song Valerie in every shoe shop, wine bar and radio station across the land, do her fans all know that it was actually written by the Liverpool band the Zutons?

It’s not as if they haven’t had success themselves: their original version went to No 9 in 2006. The year before that they were nominated for a Brit, and the year before that, the Mercury prize. Their sing-along-plus-saxophone formula is always a winner at festivals and they are about to release their third album. But when the producer Mark Ronson put a horn section behind Winehouse’s sassy vocal and released it at the height of her tabloid troubles, it got massive. It peaked at No 2, her highest chart position, and has spent 30 weeks in the Top 40.

“That just took on a life of its own, that Valerie song,” says Dave McCabe, the lead singer with the Zutons, sitting in a café in Liverpool. He wrote it, “but I don’t even think of it as my song any more. It’s out there now, it’s in the X Factor world. The weirdest thing was turning the telly on and seeing somebody doing it as their audition song. And little kids singing it on that Oliver programme too, apparently. It’s like How Deep Is Your Love.” He stops, smoothes down his greasy waves of long hair and smiles humbly. “Well, maybe not quite as good as that. But it’s one of Them Songs.”

Is he annoyed? No, no, he says. He’s flattered, he’s chuffed, and when Mark Ronson met him and said, “Thank you for the song”, McCabe told him that he should be the one doing the thanking.

He’s met Winehouse too, briefly. “She didn’t seem off her head or anything, she weren’t falling over. I said, ‘Nice one for covering our tune,’ ’cos it was her idea . . .” He trails off. Despite his trying to hide behind his hair, somebody he knows has come over to speak to him and Sean Payne, the band’s drummer. In Liverpool, the Zutons are heroes.

Indeed, they are playing at the Liverpool Sound concert alongside Paul McCartney on June 1, the day before their third album, You Can Do Anything, comes out. The show is part of the European Capital of Culture 2008 celebrations.

As for finally meeting Macca, these two actually had the chance some years ago when they were studying at his Liverpool Institute for Performing Arts (Lipa), but they turned it down. “He was handing awards out but I didn’t want one,” McCabe says.

I am baffled by his reticence until Payne steps in to explain. “We did a New Deal [Welfare to Work] course there but it’s not the real Lipa, just the dole side of it. You don’t get to use any of the studios or anything – it just gets you out of shit with the Jobcentre. At the end of the year, Paul McCartney comes and hands out your certificates; it’s like, thanks for being on the dole for another 12 months.”

Ringo is their new mate, though – he came to see them in the Los Angeles recording studio where they made You Can Do Anything and happily informed them that he was in a lot of trouble back in their home city, having informed the media that he missed nothing about the place. Zutons fans needn’t worry about this lot decamping to LA though – McCabe declares gloomily that “Hollywood done my head in”.

Later on we meet the rest of the band for a photoshoot and while Payne is chatting to his girlfriend, Abi Harding, the band’s saxophone player, their lead singer has borrowed her mobile to chat to his mum about something that needs washing. He doesn’t live with her – rumour has it that the proceeds from Valerie alone have bought him a new house, though all he says about this new unexpected income is that “every little helps”.

And if his mother’s laundry skills aren’t enough to keep him in Merseyside, the stories of his mates’ skul-duggery are. He writes songs based on their confessions about their lives – the new album is thick with song titles such as Dirty Rat, Family of Leeches, You Could Make the Four Walls Cry and Don’t Get Caught. Payne says they have always wanted to make “stories to dance to”.

Valerie was written about a friend of the band, too, although it’s been widely misinterpreted. “I always write about trouble and mischief,” McCabe says. “I haven’t got a girlfriend and I’m not in love or anything so when I get one I’ll probably write a few loving songs, but Valerie is definitely not a love song, even though everyone thinks it is. It’s about our mate Valerie getting done for drink driving and [about] telling her to come and see me, give her a hug, kind of thing.” Did she mind about her misdemeanours being celebrated in song? “Er, she was a bit freaked out by it when we played her it, yeah. ’Cos she’s got ginger hair too. It’s obviously her, it’s very literal.” But surely it’s an honour really?

Perhaps not. “People won’t tell me things any more. Me mate always says to people: ‘Don’t start pissing Dave off ’cos he’ll start writing songs about you.’ But I think life’s full of funny things to write about – you’ve just got to use it wisely.”

The Zutons’ You Can Do Anything is released on June 2 2008

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