Waiting for Nick Cave is, at best, unsettling. It's a stormy morning and I'm at the light-filled East London house/studio of the artists Tim Noble and Sue Webster. The Australian master of brooding, lyrical rock music is stuck in traffic. Nobody wants to admit it, but we're all nervous.

Noble and Webster, two of the original Young British Artists, have worked as a partnership for ten years (and are now about to marry). Their expletive-littered neon signs and sculptures built from rubbish take pop art to an extreme and have made them highly bankable. They built a bespoke light sculpture used for the cover image of Nick Cave and the Bad Seeds' new album Dig!!! Lazarus Dig!!!, which now lives in the basement of their building and looks like what might happen if you fused conceptual art with a mobile disco. They're nervous because they are huge fans of Cave, and he's coming to their house.

I'm nervous because in the last interview he gave, Cave's response to most of the questions was: “Google it”. It seemed to say something about the level of respect he has for the journalistic craft.

Then he arrives. Cave has said that being a celebrity means accepting that the mood of the room will change as soon as you enter it, and he's right: with his cadaverous frame and metallic stare he cuts an imposing presence. But then he asks for advice on how to use his new iPhone, which destroys the illusion somehow. Soon the conversation moves to funerals (Cave wants to be buried naked in a Perspex coffin), taxidermy (Noble and Webster have a collection of stuffed animals), and how they all ended up working together. “It was two years ago,” says Webster. “I wanted to see Nick Cave and the Bad Seeds for my birthday and found out they were playing in Reykjavik, but it was sold out. We had recently cooked a lunch at our studio for all these rich women who were patrons of the Guggenheim Museum and one of them was from Reykjavik, so I contacted her and asked if she could get me a ticket. She didn't have a clue who Nick Cave was, of course.”

“What do you mean ‘of course?'” interrupts the imposing presence.

“Then I got a call out of the blue from the President of Iceland's office inviting me to dinner. It turned out that this woman, Dorrit Moussaieff, is the President's wife. And when we turned up for lunch Nick was there.”

“It was a bit of a blind date,” interjects Noble. “He invited everyone to his concert afterwards.”

“I didn't know anything about them, but they gave me a book of their work,” Cave says. “I liked the electric signs they had made and thought: if you want your name up in lights these are the people to call. A couple of years later the album is ready and the title is Dig!!! Lazarus Dig!!! That's a command, something that needs to be shouted out, and I thought of Tim and Sue. I have enormous trust issues, but it felt good to let them get on with it without me breathing down their neck. All I did was give them the title.”

His trust seems to have been well placed. Cave loves it, even waxing lyrical about the wires sticking out of the back. “The wires are telling you: somebody built this thing. It's the same reason we tend to use the first or second take of a song rather than the third or fourth. They may not be perfect, but they capture some sort of essence.”

Cave makes a vague moan about the amount of press he has to do, but one feels that it's just out of habit. By the time Noble and Webster suggest that they all work together again he's clearly enjoying himself - and intimidating nobody.

“Will you play at my wedding?” Webster asks, after getting Cave to sign her favourite Bad Seeds album.

“It might be difficult to convince the others in the band,” he replies, hesitantly. “Why don't you get a mini Bad Seeds to do it?”

“What, midgets?”

“No, I mean a tribute act.”

“Can't you just come along and play piano?”

“Surely you don't want me moaning away at your wedding...”

Cave is more open to Webster's suggestion of a collaboration. He mentions that taking his kids on the school run has become rather embarrassing because of the number of Nick Cave posters they pass, and Webster suggests they make a video out of the experience. “You could film it on your iPhone,” she says.

He looks at his new gadget, and nods his head slowly. “That's not a bad idea, actually...”

Dig!!! Lazarus Dig!!! is released by Mute

Editor's choice

• Exclusive: Listen to AC/DC's Black Ice
• Burning Bush with W
• Boy George on sex, drugs and Amy Winehouse