They're an odd couple, shackled by luck, integrity and similar dysfunctional upbringings, destined to test the limits of public acceptability. Here they sit, side by side in a suite, Johnny Depp and Tim Burton, who have made six films together since Edward Scissorhands in 1990, flogging their latest apparent contradiction - an R rated slasher musical Sweeney Todd: The Demon Barber of Fleet Street, with stars who have never sung before, replete with expertly slit throats and throbbing with operatic extravagance. They look uncomfortable. "I've never been any good at selling a movie," says Mr Depp. "Talking coherently is not my speciality. Nor his," he adds, pointing to Mr Burton.

Mr Burton groans. "I can't watch my films. I have no conception whether they're good or bad." His partner, and mother of his two - one about to be born - children, Helena Bonham Carter, who also stars in Sweeney Todd, says he and Mr Depp looked like brothers as they both had "big" hair. One allows for wifely myopia. Mr Burton is an eccentric bear of man, a normal-looking bloke - he and Helena are known as Bag Lady and Scruffy.

Boyish Depp is androgynously sensual - face sleek, albeit adorned with a goatee; he speaks slowly and softly with a fine line in heterosexual camp. His dishevelled jeans, filthy shoes, necklaces, bracelets, rings - a skull and crossbones, gold signet, platinum with diamonds - sit incongruously beneath a brown fedora with which he fiddles nervously. Mr Burton whispers, "He has his own dress sense. It doesn't always work." Mr Depp seems genuinely to be a reluctant star in the "celebrity" firmament. "I've gone out of my way to avoid being turned into a Hollywood 'thing', and make a conscious effort to ensure they can't label me. It's probably a combination between being hard-headed and ignorant. There would have been an easier route, for sure. I didn't ask for fame, stardom, or adulation. Certainly you want a little bit of dough to pay the bills. But for years I was very successful at being a failure - for some reason an employable failure."

Both he and Mr Burton reinvent themselves using childhood as a template even though they're now 44 and 49 respectively. They echo each other's vulnerabilities and both remain popular without compromising their subversive and eclectic enthusiasms - Mr Depp for contrariness and Mr Burton for the macabre, although he loathes being called "dark". "It's such a cliché and makes me feel cheap and lazy - even if I do end up doing something like that. But ask anyone who knows me - it's really not true. They label you in Hollywood, and I remember that happening as a child. I felt a foreigner in my own neighbourhood (Burbank, California)." He loved watching horror movies, convinced himself that suburbia looks normal but has a dark side.

Mr Depp was also an outsider. Born in Kentucky, he moved to Florida with his parents who divorced when he was 15, dropped out of high school and went to Los Angeles with a band, The Kids. When they broke up he took any acting jobs he could, drank heavily and was into drugs - "self- medicating", he calls it. He co-owned the Viper Room on Sunset Strip in West Hollywood outside of which his best friend, actor River Phoenix died of an overdose. He married, briefly, a fellow musician Lori Anne Allison, and subsequently became engaged to Winona Rider as well as to Kate Moss and Jennifer Grey. Now the tattoos are of his two children by French actress and singer Vanessa Paradis - daughter Lily-Rose, eight, and son, Jack, five... He says he's settled and no longer has to be drunk to speak to people.

He was sober when he tried to cancel his first appointment to meet Mr Burton in a coffee shop to discuss Edward Scissorhands. The studio wanted Tom Cruise for the part. "I was a million per cent in love with the character because I knew him," says Mr Depp, "but I was a TV actor (in 21 Jump Street as an undercover cop in a high school). "They shoved this image of me as a 'poster boy' down the throats of America, and it was the furthest thing from me it could have been. I'd had enough rejection in my time and didn't want to cope with any more from Tim. Now I'd jump at anything he asked me to do - even ballet."

Their collaboration in off-beat films was interrupted by what Dustin Hoffman described to me as "the tragic accident" of the three Pirates of the Caribbean hits. "My contribution is to play a part (Jack Sparrow, the high seas bandit). I can't say I did well - although the films did. I just did my job." He was nominated for a best actor Oscar for The Curse of the Black Pearl in 2004, and also the following year for Finding Neverland. "There's no way of making sense of that. It can't be your driving force although I imagine some actors base such importance on it that it becomes part of their goal.

"Marlon Brando (with whom he worked on Don Juan DeMarco in 1995) had the best outlook. He said it's a strange job for a grown man, and it is. Sometimes he moaned, 'I hate acting' - but he didn't really. I can't speak for him but it seemed to me that he got all that adulation for being a fake who tells lies for a living, and he'd spent time with men like Martin Luther King and the Kennedys and for him to be called a great man was ridiculous. My attitude is I've had some really bad jobs, and this isn't one of them. There's an occupational hazard which can be fatiguing - all the hoopla where they try to stop you living a simple life. You're followed everywhere or looked at as some freakish oddity, which is even more disheartening."

The money and adulation must have changed him, though. "You never see your salary. You don't go to the bank and look at what you've got."

"It's a good idea, though," chides Mr Burton, implying he could be conned.

"Maybe I shouldn't have said that," mumbles Mr Depp.

Their latest collaboration, an extremely gory adaptation of Stephen Sondheim's musical is a surreal horror spoof, about a barber who turns serial killer after being wrongfully exiled. He teams up with Ms Lovett (Helena Bonham Carter) who grinds his victims into tasty meat pies. "I'd seen it done in a politically correct way which softened it. It's necessary to have blood flowing because it's over- the-top melodrama, and my inspiration comes from old horror movies."

He says the great thing about working with Mr Depp is that he doesn't bother to look at himself. "It keeps things moving when there's no vanity. He's a character actor in a leading man's body." Mr Depp adds, "If Tim wants me to see Sweeney Todd I probably will. I've seen Scissorhands, but not Charlie and the Chocolate Factory. I have a really hard time watching myself, and it's getting worse. I can't tell whether my work is good or not. I get too freaked out watching it. Everyone has some degree of vanity - You need it just to brush your teeth and walk out the door in the morning. But as an actor you have to throw that all away and go 'Whatever'."

"I've been pretty lucky with him," says Mr Burton, "and, boy, it's been so much fun. We don't analyse it. We just go 'OK, let's do it'. When we're working I see him all the time, but apart from that we barely meet. It's one of those true friendships where you start where you left off, whether it's once a day, or once a year." Surprisingly, he claims he doesn't know if Mr Depp is married to Vanessa Paradis. "I don't think they are. I treat them like a couple. Helena and I (who met in 2001 when he directed her in Planet of the Apes) feel so married we never got around to doing it, but I'm thinking about it. I'm a late bloomer."

Mr Depp is godfather to their son, Billy, four. "Johnny had children before us and it was interesting to see the subtle changes in him. It's not as if he turned into 'father knows best', but I could see the joy it brings to a person. It makes you more sensitive. I've often read that artists spend their life trying to get back to the simplicity of childhood. You see the world fresh again through your children's' eyes, and it's quite beautiful."

Mr Depp's first love was guitar playing (he didn't want to be a front man) so I suggest he's really a failed musician. "Yes," he agrees. "And I might be a failed actor, too. Who knows? I'm still a musician. The joy of falling in love with a musical instrument is that it will never go away and you won't stop playing. Am I happy with my singing in Sweeney Todd? I'm happy it's done."

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