Damien Hirst steps out of New York's Four Seasons Hotel leaving his luxury room and designer bottles of water behind, to pretend, for the benefit of our photographer, to be hitching a ride this October morning to Glastonbury, the legendary music festival that takes place several thousand miles away in June. It's his idea and a pretty funny one. Aside from the scrawled sign in his hands, everything else is wrong. The backdrop of Madison Avenue is wrong, and so are his Prada specs and Helmut Lang trousers, which wouldn't last five minutes in the West Country mud.

Minutes before, Hirst was complaining how people don't recognise him. It doesn't matter that, at 37, he is still Britain's most talked about young artist: the prophet of Britart. "They" (the public, the media, the art world) expect him to be "shaggy" and to fit the image that clings to him of the hooligan iconoclast who whips out his willy in pubs and brings boozy mayhem to the Groucho Club. But today, at least, he is all Manhattan cool. And this is a strictly personal trip – no openings – to meet some friends' new baby. He is the godfather.

"I don't really look myself," he reflects. "People have a different idea of what I look like." This only matters, he says, when he can't get into private parties. A few years back, the bouncers barred him from a party at Pravda, the fashionable New York club, that was being thrown for an opening of his work at the Gagosian Gallery. "I said, 'For fuck's sake, it's my party.'" But things only got worse when he lost his temper, he recalls. Another time, in Italy, he failed to get into a Guggenheim party because someone else feigning to be Hirst got in before him. "Everyone was running around asking what Damien Hirst looked like!"

Today, he should be shaggy, caked in dirt and with matted hair, if he really wanted to play the part. Because Glastonbury, that much-loved annual orgy of music and outdoor hedonism, is what we have met to discuss. He used to go every year and adored it. The music, the rain-sodden Somerset muck and the escapism. "It's great, you should go – if only for the moment when you get back home, and get on your hands and knees, and kiss your own floor saying 'I survived Glastonbury'. It's the best bit. The festival is just a completely different world for a few days, entirely separate from the rest of the world."

Audiences in Britain are about to be given a further insight into Glastonbury life in the form of a theatrical tribute to the festival. The play, which opens next week in Cardiff and will tour the provinces until mid-November, is called simply Glastonbury. Written by Zoe Lewis and directed by Keith Allen, the actor and bon viveur who is an old friend and co-conspirator of Hirst's, the work is generating plenty of excitement, not least because the action takes place in a 50-metre tent – and Hirst is the set designer. Don't expect a stage (actually there will be two circular stages that revolve throughout the play) adorned with Hirst-brand works – you know, cows in tanks of formaldehyde or paintings with coloured dots. Instead, there will be a backdrop covered in a collage of photographs of past festivals; there will be some brushstrokes, but otherwise this will be a departure for Hirst.

"There are no spots or dead animals or that sort of stuff," he confirms. "I just got in there and created a Glastonbury atmosphere inside a tent. Gradually, the set just gets dirtier and filthier. It starts out quite neat and ends up covered in mud." The play is about seven characters, who turn up at the festival – from a headliner teen-star to a 17-year-old adolescent – all with clashing expectations and hopes. "There are mobile phones and sex and death and in it, and I think it will be really funny," enthuses Hirst, adding that it is the die-hard disciples of Glastonbury who should love it the most.

Not that the project has been all smooth sailing. There have been budgets to respect and serious technical problems that finally led to the opening night being pushed back by a week. "The last conversations I had were nightmares to do with electrics and lighting and water and mud. The technical people were saying, 'Please don't do this', and we said, 'No we have to do this'." Hirst, for example, has insisting on rain falling during one scene, causing instant panic that actors and audience alike might risk severe electrocution.

So do we have a new Hirst now – man of the theatre? In just a few years, he has zipped through several other mini-incarnations, beyond the business of being a millionaire art-world phenomenon. He has made a short film (Hanging Around), directed a pop video (Blur's "In the Country"), and plunged into the opening of two London restaurants (Quo Vadis and Pharmacy). He also joined in the creation of Fat Les, the supergroup co-starring Keith Allen and Alex James of Blur. Hirst is the proud owner of a gold disc of the group's football anthem, "Vindaloo", which is still a favourite on the terraces. But in fact, he sees the Glastonbury project more as a one-off bit of fun. Both Allen and the playwright, Lewis, are his mates and, he says, he loved the work. It is the first piece of theatre to look at Glastonbury, even though the festival remains, after all these years, a unique, rambunctious event on Britain's cultural calendar.

"This was just something that I really wanted to do. I get asked to do a lot. One thing I get a lot of especially is people asking me to do an opera. But I have never been really interested. If something comes along that is interesting, then maybe I'll do it. They phone up and ask me to take photographs of a pair of my shoes. Magazines are just insane. I get ridiculous requests, for socks, shoes, constantly. It's maybe one hundred a week, and basically I say no to everything."

And Hirst, after all, can afford to wander off down new avenues occasionally, because his success has made him rich. He lives most of the time in Devon with his girlfriend Maia Norman, who is from California, and his two small children. He has studios in Stroud, Gloucester, and now in London as well. He wouldn't mind having a place in New York, too, he muses.

Everyone knows that he sold Hymn, a 20ft anatomical giant, to Charles Saatchi for £1m in 2000. Actually, he admits, he made four of these monsters. And they all sold for the same price. Isn't that disgusting, I ask? A million for what was really a blow-up of a toy he found in his boy's room. "Not really," he says, adding, without any kind of defensive tone, that making pieces on that scale costs money. He is currently in the early stages of producing giant crucifixions involving cows. He says it is his new religious phase. And he adds that he has spent £750,000 on the project already, and that is just for the tanks in which the pieces will be housed. (Yes, more tanks.) Each one will be 26ft tall, and that's a lot of glass. As for the cows, he hasn't decided yet if they will be fake or real carcasses.

Death is something that has always interested him. Death and corpses. "In England, we don't do death very well." But today, we seem to get snagged on this money thing. "The other day, my son came home and said 'Daddy, a girl at school said to me that you are rich', and I was like, 'Where did you get that from?'" Can't imagine. But the childish observation seems to have bothered him. Hirst, this boy from Leeds, is adamant that getting lucre was never his game. Not in itself. "I think my desire was more to be famous than to be rich. I think a desire to make art and be famous is like a desire to live forever. Which is what art is all about, really." It is important to Hirst that his works live on far beyond his death. That is where immortality becomes a possibility for artists. If anyone buys their work.

But, his own wealth aside, he wants to talk about money and its role – good and bad – in art. He admits he is lucky to have the money to do what he wants with his work. People pressure him to scale back his projects all the time, and he can afford to ignore them. And it allows him to be a perfectionist. "Constantly, guys want certain things, but the thing that they want boils down at the end of the day to things that cost nothing to make but you can sell for loads of money. They say if you make it three feet smaller it would be so much cheaper, but you go, 'Yeah, but it wouldn't have the same impact'." It's vital to Hirst, for instance, that the crucifixions are 26ft tall. Not 23ft tall. "They have to got to be up there, right above your head or it won't work, even if the tanks are insanely expensive." Clearly, most artists don't have the same kind of resources and often their artistic ambitious are compromised by it.

But he argues that the opposite can be true. There is a temptation for people like him to spend too much. "It can cause you lots of problems creatively, because you try to solve problems by throwing money at them, which can equally lead to disaster. A lot of people overdo it – paint too big. They go for a canvas that is 50ft by 50ft when they could get something that would be better if it was the size of Rembrandt etching."

And is there such a thing as too much notoriety, something else Hirst has more of than any of his peers? His answer is the same. "Some people deal with fame in a terrible way," he says. He recalls the years – call them "the Groucho years" – when he would hang out mostly with celebrities – Elton, Bowie, Joan Collins et al. Ensconced in his converted farmhouse, he is past that now. He is interested only in friends, he insists. "You have to be humble; it's very easy to become a victim of your own success." Touchingly, he tells how Maia attempts to bring him down a notch every now and then with "Who-the-hell-do-you-think-you-are?" type comments. But sometimes even she can't resist the power fame affords. "Then I'll see her on the phone saying, 'Yeah, can I have a table for two please for Damien Hirst, yeah, the Damien Hirst'," he laughs.

And sometimes Hirst makes headlines in ways he regrets. Most recently, he caused a furore when he commented in an interview that the carnage visited by Osama bin Laden on the World Trade Centre had constituted art. He had to publicly retract the comment. "That was kind of a calamity. I made the mistake of saying two words in the same sentence that should never go together, congratulate and terrorists. In America, obviously, you can't say that."

Anyway, he is sure of one thing. He will be humbled royally at the opening of Glastonbury in Cardiff on Wednesday. The moment will not necessarily come with the performance itself. Or even when it is reviewed in the papers. No, Hirst will be reminded that he is a mortal like the rest of us when he arrives for the opening night party and no one will let him in. "I will go with someone who will be able to get in. And I will go early. I think that's the secret."

'Glastonbury' is at Pontcanna Fields, Cardiff (0871 2200260) from Wednesday until Saturday and then tours. 'The Independent' is the play's media partner