Alice Cooper is telling me about a goat. At the Bloodstock festival, which he has just been to, everyone, he says, was talking about a goat. “The story,” he says, with a smile that shows his big, white, even teeth, “is that someone's sacrificed a goat in their dressing room. And I,” he says, and his smile gets bigger, “am going, 'why wouldn't you do that on stage?'”.

The goat, it turns out, was already dead. It was actually just a goat's head, from a local butcher's. But the goat sounds a bit like the chicken that helped to make Alice Cooper Alice Cooper. It was thrown on stage in 1969, when Alice Cooper was the name of a band and Vincent Furnier was its lead singer. Feathers flew. Blood flowed. A myth was born.

Vincent Furnier, who has called himself Alice Cooper since the band broke up, didn't actually bite the head off the chicken. “I threw it at the audience,” he tells me, “the audience threw it back and the next day in the paper I read that I'd killed the chicken. I thought, well, the deed's been done, and people love it. I never said I did it or didn't.” Technically, that's true. Vincent Furnier, who I'll try to call Alice Cooper, even though it does seem a bit weird to call a man Alice, didn't say he did it, but he certainly let the world believe he did. He did that because his agent, Shep Gordon, who's still his agent 43 years on, told him it would be good “for publicity”. And it was. Mary Whitehouse tried to stop the band from coming to Britain. The Home Secretary tried to get the British tour banned. But the fans loved it, and sales soared.

The fans loved it, too, when Furnier and his band members started performing with boa constrictors. The snakes didn't die, or at least they didn't die on stage. One died of pneumonia. Another spent its last hours in a toilet drain in a Tennessee hotel. But most of the blood, and gore, and death on stage when Alice Cooper performed wasn't real. The babies with their heads chopped off weren't real. Nor were the live executions. Cooper (the man) has, he says, returned from the dead “about 60,000 times”. He'll do it again in his new tour, for Hallowe'en.

“We're doing better tours now than we ever did,” he tells me, in the tones some Americans use when you ask them how they are and they tell you that they're “great”. He looks pretty good, it's true, sitting on this sofa, in a posh boutique hotel. The black jacket, and black T-shirt, and dyed black hair, and crucifix, don't make him look any less pale, or wrinkled. But for someone who has been on the road for quite a lot of the past 48 years, he looks pretty damn good.

But better tours now than he ever did? At 64? “Oh, absolutely,” says Cooper, calmly. “When I was 30, I was a mess. I was drinking a bottle of whisky a day. I did shows that weren't anywhere near as good as the shows I do now.”

OK, I say, as I try to think of a way to put this diplomatically. But surely there would have been a spirit of rock'n'roll in those early shows that wasn't quite as strong in them now?

“Absolutely,” says Cooper again. “And in some ways,” he adds, as if he's keen to help me with my case, “it was better, because it was more guerrilla. You couldn't come out there wimpy, you had to come out there strong. It was just rock'*'roll and in your face, but, like you said, the drunk edge gave it a real power.

“We were kind of looked down on by other bands,” he says, “but only because we were so theatrical and sensational that people said, 'well, take your theatrics away and you're not a good band'. We were every bit as good a band as anybody out there. In our heads, we were competing with Led Zeppelin, and the Rolling Stones, and the Beatles.”

Because I'm English, I feel like blushing, but it's true that those early hits – “School's Out”, “Eighteen, – had a raw power that wasn't all that far from some of the best hits of some of their best peers. It's also true that Paul McCartney, John Lennon and Bob Dylan loved what they were doing, and so did David Bowie and Elton John. Johnny Rotten (now John Lydon) even called Killer, which came out in 1971, ”the greatest rock'n'roll album of all time“. He said Alice Cooper was the Sex Pistols' biggest inspiration.

It all started with the Beatles. It started, in fact, with a band called The Earwigs, who were, says Cooper, “a parody of the Beatles”. Furnier, and some of his classmates at school in Detroit, formed it, he says, as “a joke”. They entered a talent show, and got “the bug”. They couldn't play instruments, but they learnt. After a short spell as The Earwigs, they called themselves The Spiders, and then The Nazz. When the band which by now was made up of Furnier, Michael Bruce, Glen Buxton, Neal Smith and Dennis Dunaway – found out there was another band called The Nazz, Furnier suggested the name Alice Cooper. He liked, he said, the contrast between the band's image and the wholesome name.

“Eighteen” became a hit in 1971. “School's Out”, which came out the following year, was an American Top 10 single, and a British No 1. Billion Dollar Babies, which came out in 1973, was a No 1 album on both sides of the Atlantic.

Furnier wanted to go bigger, and wilder. He wanted more theatre, more shocks, and more gore. His other bandmates didn't. The band split. Cooper took the name (with their permission and paying royalties) and decided to go it alone. In 1975 he brought out his first solo album, Welcome to My Nightmare. The film of the name, which has been called the first rock music video album, was full of giant spiders, dancing skeletons and faceless demons. It also presented Alice Cooper the man as less a rock god, and more a vaudeville villain.

Wasn't there a part of him, I ask, that has actually been parodying Alice Cooper ever since? Cooper smiles his charming smile. “Oh, absolutely,” he says again. “And I treat Alice in the third person, because I can't take him anywhere. He belongs on stage. But there was a grey area for quite a long time when I didn't know where I began and where Alice ended.” Well, yes. He has said that in interviews quite a lot. But my point, I say, is that the heart of rock isn't parody. It is something else. So can he really call this rock?

“Yes,” says Cooper. “If you take the image away. I'm still in a bar band, because I've never grown out of it. I'll be the last guy who ever looks at the band and says, 'turn it down'. But I love the character. I always say Alice Cooper's my favourite rock star.” Oh dear. I feel like blushing again. But isn't it, I try again, like having a puppet between you and the audience? “It is,” says Cooper politely, “but he's a really fun puppet. My fans,” he adds, “don't want him to be human. They want him to be this other-worldly character.”

At this point, Cooper's wife walks in. He met Sheryl Goddard, a dancer and choreographer who performed in his show, when he was dating Raquel Welch. He left Welch and married her. But in 1983, when he was well on his way to drinking himself to death, she filed for divorce. He dried out. They made up. He has, he has often said, “never cheated on her”. Now she travels with him, and watches nearly all his shows. His eldest daughter, Calico, even sometimes performs in them. Alice Cooper, it's clear, is something of a family business. So does he think, I ask, once Sheryl, who looks very young for a woman of 56, has gone to do some shopping, that having this character as a part of his life has done him any harm? Cooper nods.

“It did,” he says. “I didn't know where Alice stopped and I began, and that was because of alcohol. I lived in that era of Keith Moon, John Lennon, the Hollywood Vampires drinking club. All our friends,” he says, “were dying at 27.”

He is, I tell him, smiling. “That,” he says, still smiling, “is because I got through it.” Yes, I say, but they didn't. “If you're a rock star,” he says, “you're supposed to do that. There are no rock stars any more. They're lacking in so much testosterone. I keep looking for the 17-year-old kid who wants to hang his guitar down here and play it from his crotch, not his brain.”

Well, yes. To me, today's rock stars all look like librarians. But he's the one who's meant to think that all that hard living was a sin. He's the one who was the son of a car salesman who became a missionary to the Apache Indians. He's the one, in fact, who calls himself a born-again Christian. Would he, I ask, have described himself as a Christian during the years of excess? “No,” he says, “because I wasn't living the lifestyle.” But did he believe it all? “Yes.”

If he really believed it all at the time he was drinking a bottle of whisky a day, and sleeping with every groupie who threw herself at him, he must surely have thought he was in trouble? “Oh, absolutely,” says Cooper again. “When I was at my height, I thought: 'If this plane is going down now, I'm going directly to Hell. I know that I owe my soul to Christ, but I'm betting that I can go one more day.'” When he finally sobered up, he realised he couldn't. For a moment, he thought he would have to give up being Alice Cooper, but luckily his pastor disagreed. “He said,” says Cooper, in the way you say something when you think you've won an argument, “'does God make mistakes?'”

Does he believe the Bible is the literal word of God? “Yes, true each word”. Does he believe the Old Testament? “I believe the Old Testament explicitly.” So he doesn't believe in evolution? “I believe there's evolution inside the species.” And does he think that the world was created in seven days? “Oh yes.”

God, says Cooper, “has a plan for everybody. I look at my life and I think, 'how is it possible that I didn't die?'”

So was it, I say, God's plan for Jim Morrison, Jimi Hendrix and Brian Jones to die? “The question,” he says, “is why wouldn't God let that happen?” He tells a long story from the Bible about a tower falling down. In the story, it seems to have something to do with choosing sin over God. “If God wants to save you from getting hit by a bus,” he says, as if this clinches the argument, “he will.”

But what, I ask, does he think about the bit in the Bible that talks about it being less difficult for a camel to pass through the eye of a needle than for a rich man to enter the kingdom of heaven? The eye of the needle, he tells me, is a gate in Jerusalem. Which, he implies, it wouldn't be all that hard to get through. “It's because,” he explains patiently, “we are so intoxicated by wealth and what it buys”.

Are we? “Speak,” I hear myself saying a little bit rudely, “for yourself”! I'm not the one who has made millions with a vaudeville villain, or the one who, according to all the accounts I've read, set out to make millions. “A motivating factor,” says Cooper, who grew up in a trailer park, and says they had “one present” at Christmas, “doesn't mean rich people go to Hell. You can make anything an idol. I spend more time playing golf than I do in church.” Alice Cooper certainly does play a lot of golf. He plays six days a week, and every morning on the day of a show. After that, he says, he'll go back to his hotel for lunch, and then he'll go shopping. He gets stopped, he says, “all the time”. He signs “everything”, takes “every picture” and then has “a nap”. After that he watches kung fu movies, and after his movies he throws Chinese knives. But when the curtain goes up he's Alice. “My posture changes,” he says, and as I watch, it does. “Now,” he says, and for a moment I'm not quite sure who I'm looking at, “I'm this character, and for an hour and a half I do not break this character. I know Alice so well that he's my defence.”

Well, sure. After 40-odd years of playing him, he probably should. But doesn't he think it might be interesting to develop the character? Doesn't he, in fact, get a little bit bored? Cooper's smile freezes. “People like Alice so much, why would I want to invent another character? You think I get bored with it? I don't. I think Alice is infinitely fun to play.”

And doesn't he, I ask, get a little bit bored of hearing himself tell the same stories? There's the story of the chicken. There's the story of meeting Salvador Dali, who said he thought his show was surreal and made a sculpture – a chocolate eclair covered in ants – of Cooper's brain. There are the stories about Groucho Marx, and Fred Astaire and Mae West, who, he has said, took him “as their mascot”. There's the story about Elvis, who asked him to shoot him and handed him a gun. They're great stories, but he has told them quite a lot. “I always say,” says Cooper, “that I never let the truth get in the way of a good story, as long as it doesn't hurt anybody. But the funny thing was, the more extreme stories were the ones you didn't have to elaborate on.”

The life, it's clear, has been as full of drama as the shows. But what about the art? And what does he think about the art? Which, for example, are his best albums? For the first time, Cooper looks floored. “Oh boy,” he says, “there's an argument all over the place. Love It to Death, the first album with [producer] Bob Ezrin would have been the first definitive album. Welcome to My Nightmare: that was a genius album. The Last Temptation: I thought that was a really good album. Along Came a Spider was a really good album, and Brutal Planet and Dragontown.”

OK, I've got the picture. Or at least I think I'm getting it. He doesn't mention Welcome 2 My Nightmare, which he released last year, his 19th solo album, but perhaps if I give him long enough, he will. And what does he do when he's not being, or talking about, Alice Cooper?

“A lot of things I do are very gay things. I love Broadway. I love dance. I love shopping.” Right, I say, still slightly reeling from the “gay things”. And what, as a born-again Christian, does he think about being gay? “Well, everybody says this is a gigantic sin,” says Cooper, “but so is stealing a candy bar.” And then he actually does say, “some of my best friends are gay”.

Alice Cooper, it's clear, has made a lot of friends. He has made a lot of music. He has done a lot of shows. And he's nice. Everyone says he's nice. He must be nice. Does he think he's nice? “Oh,” he says, and he flashes his big, white, even teeth, “I'm the nicest guy I know.”