Helena Bonham Carter is tripping down a Hampstead street on a busy bank-holiday lunchtime, a celebrity-spotter’s dream. In a sea of groomed yummy mummies in smock tops, she looks a cross between BoPeep and Marge Simpson with a tequila hangover; which is to say, she looks whimsical, retro and ever so slightly louche. She has always been contemptuous of her prettiness, has never believed in it; the mad hair and car-crash ensembles have been her way of avoiding embarrassing flattery (she prefers teasing), part of the armour she has employed since her first big role, when she was cast, as a “terrified” teenager, by Trevor Nunn as Lady Jane Grey in 1984. The voice, too, seems a disguise, so crazy-posh in its plummiest depths, you wonder for a second if it’s exaggerated for a bit of fun. She has flakes of mascara beneath her eyes, an air of having been up too late or too early (probably both, since she is currently filming Sweeney Todd and has a three-year-old son).

She strikes me as a woman who has hit her stride after a lot of false starts, one who is enjoying being 40, a rare sentiment among those accustomed to admiration for their dewy, youthful beauty. Bonham Carter’s six-year partnership with the director Tim Burton, father of her son Billy Ray – they are kindred spirits, with their gothic taste and aversion to combs – seems to have given her the confidence that was her birthright. She is, after all, the great-granddaughter of the former prime minister Herbert Asquith and a member of a great Liberal clan. Or maybe she was just slow to grow up, stalled by her closeness to her parents, with whom she lived in Golders Green until she was 30, and by starting big-time acting young, and so becoming an adorable, talented baby for various mentors. For chocolate-box romantics, A Room with a View will always be her defining movie, but she has spent the past decade escaping the shade cast by Lucy Honeychurch’s parasol, and emerged as an actress in her prime. Clearly born to play schlock-horror spoofs and clever bluestockings, Bonham Carter is metamorphosing into a great English maverick, heading for a feisty middle age of which EM Forster would be proud, and with more in common with her indomitable grandmother Violet Bonham Carter than she cares to acknowledge.

Today, she is so happy with the sunshine and her boys, and whatever treat rustles inside that Whistles bag slung over her shoulder, that she is almost skipping. She is dressed in a 1950s-style sundress and pink fluffy cardigan, with vintage shades; her hair is piled high in a bird’s nest studded with blue velvet bows, the work of her best friend and movie hairstylist, Carol, who has been with her since the earliest Merchant Ivory bouffants. “She is the best person at making your hair look as if it hasn’t been washed for years,” she gushes, as if that might be what anybody else required from their hairdresser. Her hair is in character today, but you couldn’t really tell. She also has the filthiest fingernails you’ve seen since primary school. Like the hairdo, they are the result of playing Mrs Lovett – maker of mud pies, and much worse – against Johnny Depp’s Sweeney Todd in Burton’s movie, which is shooting in London. The odd couple live together in ahouse around the corner, but, despite rumours to the contrary, it boasts no secret passage between separate dwellings. “No underground tunnel,” she confirms, “though maybe we should have a bridge of sighs. Tim is sighing a lot at the moment.”

It must be tough to stop being a couple on set, I say. She rolls her eyes. “The problem is that we don’t stop. Tim sighs loudly. I say, ‘What? What? What am I doing wrong?’ Johnny looks away diplomatically, or starts dusting his razor overattentively. We’re both banned from discussing the film at home. It’s number one on the list of commandments I’ve written down.” Since they fell in love on Planet of the Apes, he has cast her in four films, including Big Fish and Charlie and the Chocolate Factory. “After this, I wouldn’t work with him again,” she hoots, lying her socks off. Actually, her admiration for him seeps into every corner of our conversation, and, having spent 10 minutes with her, you can tell they are a good match: smart, alert and cackling with laughter at silly jokes. “Now I have Tim, Johnny and Billy all doing poo-poo jokes together. What a nightmare!”

For all her success, the early Bonham Carter seemed a troubled creature, living at home too long, clearly devastated by her father’s stroke when she was 13, falling in and out of relationships, including one with Kenneth Branagh. She was always articulate and outwardly assured, but still a little lost. Burton (and Billy) seems to have fixed that, and not just by making her his muse. “It looks like a clever ruse,” she admits, “getting together with a film director. Unfortunately, it’s not that simple. Tim is unbelievably disciplined about employing me only if I am absolutely right. For Sweeney Todd, it was like I had to be more right than anyone else; it was ‘in spite of’, instead of ‘because of’, being his girlfriend. I know a lot of actresses will say it’s because I was sleeping with him, but it’s not true. I had to audition for Stephen Sondheim, for God’s sake! When it’s all over, I’ll tell the whole saga of how I got the part. It was like being in How Do You Solve a Problem Like Maria? – so painful and so acute that Tim said, ‘We cannot watch this programme. We are actually living it, and it is hideous.’ ”

We are meant to be discussing her new film, Hans Canosa’s Conversations with Other Women, a savvy two-hander, co-starring Aaron Eckhart, about a divorced couple who are still in love and meet again at a wedding. “It’s about closure,” she says. “It’s a requiem for a relationship. My character needs to work out if she was right to leave him, and she does – she has moved on, but he hasn’t moved on a minute.” There was a time when she seemed to crave just this sort of role: modern, complex, sexual, mature. Of all those words, the last is the one that makes her shriek: “I have never felt mature. Anyone who knows me would agree ... Sure, I’m more interesting than when I was 20, but sadly the parts get exponentially less interesting. This was an exception.” At least age has allowed her to make her own rules: requests for her to bare more than her soul for the camera are greeted with supreme caution.

Billy was nine months old when Bonham Carter shot Conversations. She had regained her body shape, but the sex scenes were written as “head-to-toe naked”, and she refused. “Even then, I wondered if it was necessary for my boobs to be on show.” She pauses. “Though it’s true that when people have sex, they don’t usually keep their clothes on ... It was my idea to get undressed under the covers. Otherwise, my character had to be naked and get into bed, and I said, ‘Not if she’s self-conscious about her age! Certainly not when she knows he’s now with a f***ing dancer!’”

In all her musings about film, its technical aspect seems firmly stuck in mind. “We shot in two weeks,” she says approvingly of Conversations, “and on video, so we could shoot for ever – with film, you are limited to 11 minutes.” Her interest no doubt derives from sharing her life with a man whose business is light meters and special effects, especially on an extravaganza such as Sweeney Todd. “This film has made me see that I am just a cog,” she says. “Actors can get egotistical and want to use whatever prop. I’m just as bad. ‘Ooh, Tim,’ I’ll say, ‘what about this?’ But if it doesn’t help the story, forget it. I have been disobedient in the past, but I have understood that if you don’t hit your mark, you won’t get the light or you’ll be blocked.”

Sweeney Todd, his first musical, has been a high-pressure adventure for Burton, spiced with the drama of the production being halted during the illness of Depp’s daughter, now thankfully recovered. For its leading lady, the breakthrough has been learning to sing. “One audition, I sung for four hours, and Tim said, ‘No, no, that’s enough. Will you stop?’ I’ve had nine months of singing daily. Now I’ve got this skill, this instrument, and it makes me feel finally like a proper actor. I feel more self-respect.” That elusive quality is one she lacked in the past, leading to “huge complexes”, including one about not having gone to drama school. After A Room with a View, she visited a few establishments, including Bristol Old Vic, where the intention seemed to be to break her down, then rebuild her. “I thought, I won’t have fun here, so forget it. Anyway, I’ve given up the regrets, and that is liberating. F*** it. Whatever.”

Her career took off from a single photograph. In 1985, Tatler was running a feature on people who looked as if they came from a different era. Bonham Carter’s cousin Virginia was to be the Titian-haired preRaphaelite. When she dropped out, good old “Hels” was asked to step in. “It was only because I had long hair,” she says, seemingly nudging herself to remember how lucky that early break had been. “My whole career boils down to how Carol did my hair on that shoot. For most of the 1980s, I was just ‘the girl with the hair’.” She was keen to start work. After her father’s paralysing illness, his youngest child felt she ought to have an independence and an income to call her own. She laughs wickedly. “Besides, I thought, while he’s in intensive care, he won’t care what I’m doing, so I’ll get an agent!”

In the close-knit Merchant Ivory troupe, Bonham Carter became the adopted treasure, nicknamed “little thing” (in A Room with a View, Cecil Vyse calls Lucy “little thing”). Was it a comfortable family? “No, it was eccentric, Ismail never off the phone, and Ruth [Prawer Jhabvala] just typing, typing, existing on coffee and sugar, the thinnest person you ever saw.”

In her mid-thirties, Bonham Carter sometimes sounded bored and disenchanted with acting. It was all too easy to assume she was feeling suffocated by period costume, but she says the malaise, now passed, was deeper. “I didn’t think it was a serious way of making a living. Actually, I was never fed up with those period parts: they are good roles for women, all leads. I think the press got tired of me in them. It was unfair, because the dresses may have been the same, but the characters were very different.” Did she feel trapped? “Not really; it’s a myth. Directors don’t typecast you – David Fincher gave me Fight Club. Tim never typecast me. The first thing he said to me was, ‘I have a feeling that you ought to be an ape.’ Besides, you’re always going to have an encapsulating headline – for me, first it was ‘Posh great-granddaughter of PM’, which I’d been oblivious to.” Her mother, Elena, always reminded her she was also half Spanish, a bit Jewish, as red-blooded as blue-blooded; her father “pedantically” pointed out she wasn’t a real aristocrat, since Asquith had once been a down-to-earth Yorkshireman.

The highbrow Liberal clan into which she was born sounds chaotic: brilliant, sweethearted, arriving to help her mother and breaking everything in the kitchen because they were all so undomesticated. The party leader Jo Grimond, husband of her aunt Laura, she recalls fondly as “a gentle giant with a huge head, very deaf and somewhat remote. When we made family visits, he tended to hide in the kitchen.” Her adored father, Raymond, who died in 2004, was the least political of the siblings. She has still to locate her own social cause; though her cousin Jane, a Lib Dem peer, is “always tying to enlist me”, she has so far wriggled free.

Nor does she lobby much for parts. Her last effort at being proactive proved a disaster. She wrote a passionate letter to Peter Kosminsky, asking to be seen for Cathy in his 1992 Wuthering Heights (the part went to Juliette Binoche). “Actually, it was more of an essay on the whole of Emily Brontë, and he said, you must come in. I was wearing dungarees – probably not the best thing to wear to an audition for a romantic heroine. I was all wrong, and he was fumbling around, and I said, ‘Come on! What is it?’ He said, ‘Um, I think you’re a bit dumpy, that’s all.’ ” She screeches with laughter. “Luckily, I didn’t hurl myself into bulimia.”

Her great leap into the 20th century was Woody Allen’s Mighty Aphrodite (1995), in which she played a cool, unfaithful wife. “I didn’t feel happy in the part; I wasn’t mature enough. She was very sophisticated, and I didn’t really like her. I have to like my characters. I love Mrs Lovett – she makes pies out of humans, but she’s fantastic!” After Allen, she went back into a corset to play the scheming Kate Croy in The Wings of the Dove (1997), which won her an Oscar nomination. “I couldn’t not do it, the part was too good.” Whether consciously or not, she has now mastered enough gritty or comic parts to counterbalance the implausibly pretty ones: a woman with motor-neurone disease in The Theory of Flight (1998); the mother of autistic sons in Magnificent 7 (2005); as a voice in the animated Corpse Bride and Wallace & Gromit – The Curse of the Were-Rabbit. Her next project looks set to be Eleanor & Colette, with Susan Sarandon, the story of a mentally ill woman campaigning to win rights over her medication.

Recently, A Room with a View was on television when the Burton-Bonham Carters were at home, and she cringed while he laughed. Isn’t he charmed by the vision of Edwardian femininity? She splutters. “He’s not charmed at all! He just talks about my hyperactive eyebrows. For Mrs Lovett, he says, ‘Don’t move your caterpillars; don’t move your hands.’ He takes the piss out of me most of the time.” The irreverence seems to have been just what she needed, yet, for all her late blossoming, Bonham Carter is still unable to watch herself on screen. “I go into a massive depression. It takes four days to recover, and every time, I say, ‘I’m giving up acting.’ I’m very self-critical. I hate everything – how bad I look, how bad my performance is. In acting, I’m trying to get away from myself, and when I see the work, I think, ‘Oh no, after all that effort, it’s still me!’ ”

The only film she has been able to watch is Planet of the Apes, in which she wears a chimp suit, a disguise she enjoyed more than all the wasp-waisted constructions or even her own funky-fairy wardrobe; and one that taught her something. “It’s the only film in which I can understand what people might see in me. My eyes are quite kind. And quite spirited.”

As for her darling son, she insists he will not follow her into the industry she half loves and half scorns, and intermittently plans to escape. “Absolutely not – don’t go there, mate! He can be a lawyer or an accountant.” Given little Billy Ray’s arty provenance, his celebrity contacts and his parents’ collection of kitsch sunglasses, civilian life seems somehow unlikely.

Conversations with Other Women is released on May 18

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