Helena Boham Carter: After 30 years of waiting, the actress is finally playing the role of her dreams

The Sweeney Todd star talks to Nicola Christie

There aren't many parts that require singing, baking and gazing at Johnny Depp all at the same time. Maybe that's why Helena Bonham Carter is looking so happy. "It's an absolutely great part," she admits. "But I had to fight for it."

Lady Lovett, maker of the finest pies in London, is a Lady Macbeth of the musical stage who wills the man she yearns for, a barber by the name of Sweeney Todd, to cut the throats of his customers in order to provide a cheap and easy filling for her pies. The show, written by Stephen Sondheim, sent audiences wild when it opened on Broadway in 1979. Now it's causing similar excitement in movie-land, this week garnering a Golden Globe for its lead actor Johnny Depp and one for Best Musical too.

We meet during shooting, in Mrs Lovett's dressing room at Pinewood studios. On the way in, I've bumped into an alarming number of body parts – severed heads, hands with thumbs missing – illustrative of the havoc that Bonham Carter is called upon to unleash in the film. There are plenty of pots of red gloopy paint on standby, too, waiting to be slopped all over the screen.

I ask how she's enjoying herself, back on set with Depp, Tim Burton's other great muse, and godfather to her and Burton's four-year son Billy. "He's great, we're having a brilliant time." But what about her director? How does that work? "I've learnt not to talk so much and basically obey him, because he's the chief at work."

It was during the shoot for The Planet of the Apes remake in 2001 that Bonham Carter and Burton locked fates. He told her she'd make a perfect monkey, and the two have lived happily in Hampstead ever since, recently becoming the proud parents of a baby girl, born just before Christmas.

"It can be difficult living and working together. It depends on the day. Sometimes we revert to a couple and our relationship at home on set, which isn't helpful."

They can't get it too wrong too often, though, as they're still working together. Their past collaborations include Charlie and the Chocolate Factory (with Bonham Carter delivering a glorious Cockney turn as Mrs Bucket), Big Fish and Corpse Bride. For the leading man Depp, the relationship with Burton goes back even further, to the touching 1990 fantasy movie Edward Scissorhands. As the Demon Barber of Fleet Street, Depp was an instant choice for the director. Not so for Bonham Carter as Mrs Lovett.

"I had to fight for it," she recalls. "More than for anything else I've done. I've been wanting to play the part since I was 13 – when I first saw the show. Tim said, 'Well, you can try, but there's no guarantee you're going to get the part'."

Casting that swept from London to New York, taking in leading actresses of the stage and pop stars like Cindy Lauper, eventually settled on Bonham Carter. It was Stephen Sondheim who had the final say. "Tim and I both burst into tears."

As a young girl growing up in Golders Green, Helena would do her hair like Mrs Lovett and spend time locked in her bedroom going through the score and the lyrics. "I was a strange child," she concedes.

In person there's nothing strange about the actress who has become one of the finest ambassadors of British acting since her performance in the 1985 Merchant-Ivory film A Room With a View. Famed for her cut-glass vowels and smouldering delicacy, she finally swapped the corsets and fine muslins of films such as Howards End and The Wings of the Dove for roles like the cigarette-smoking bad chick Marla Singer in Fight Club and Woody Allen's pushy wife Amanda in Mighty Aphrodite. More recently, she played a Jewish mother in Paul Weiland's Sixty Six and a bridesmaid – "I wear one costume for the whole film, I'd love every film to be done on that scale!" – in Hans Canosa's Conversations with Other Women.

These days, her aristocratic heritage – she's the great-granddaughter of the prime minister Herbert Asquith – is frequently overlooked in favour of a focus on her eccentric, gothic, dress sense, fierce frankness and wild curls. She's often labelled a witch, but in person she comes across as nothing other than beautiful and intense. "But you know I do like playing a witch," she giggles.

And we've seen it; first as Bellatrix Lestrange in the Harry Potter movies – "I love that whole magical world, all the wizards and the witches" – and now in Sweeney Todd, prowling about the screen with a face caked in white slap, looking suitably rotten and hag-like. "It's a bit of a horror movie, a Victorian melodrama, but in music. It's operetta-like, actually."

It's also this year's Moulin Rouge, but instead of Nicole Kidman and Ewan McGregor cooing over each other we have Bonham Carter and Depp eating people alive, or at least baking people alive for others to eat. The story dates to 1846 when a wrongly convicted barber returns from jail. Thirsty for revenge for his wife's murder, he wields his razors to slit the throats of his customers, thus providing cheap filling for his landlady's pies. It's a story that film directors including Sam Mendes have been trying to get their hands on for years.

For the actors, it required three months of singing lessons, with Depp locking himself in a recording studio in LA to make a demo before he dared do it for real in London.

"Johnny's singing voice is very sexy," Bonham Carter reflects. He takes a role played in the past by actors and singers ranging from Ray Winstone to Bryn Terfel, and is a revelation in it – a worthy Golden Globe winner, in fact – delivering a Pirates-of-the-Caribbean-flavoured Cockney but with haunting sadness driving the role this time, rather than cocky playfulness.

"He really sings from the gut, and it's a very emotional role," reflects Bonham Carter, admiringly. "His singing is very naked and very touching."

Depp is equally keen to gush about his on-screen wife. "She's very brave," he says. "Without question, that's the toughest part in the movie and she beautifully made it her own. She's made Mrs Lovett vulnerable, horrific, funny and sweet."

Bonham Carter's character is a lady who's not really a lady but wants to be one, craving a man who is so intent on revenge that he never notices her. "I saw her as totally amoral, but full of zest and full of life," says the actress. "She's a survivor. But the main thing that motors her, the main thing that defines Mrs Lovett, is that she's tragically in love with somebody who doesn't love her back."

The cast is rounded out by Alan Rickman, Timothy Spall (both of whom had singing training at Rada so had an easier time of it) and Sacha Baron Cohen, who came in and sang the entire score of Fiddler on the Roof at his audition to convince them to give him the part of the rival barber Pirelli.

"It's been a very special experience for us all," reflects Bonham Carter, before smiling wickedly at an apt choice of culinary metaphor: "For Tim this film has been marinating for 20 years."

'Sweeney Todd' opens on 25 January