There are moments in every actor's life where the sheer ridiculousness of what they do is rammed home. And in those moments, usually with big hair and too much make-up, Helena Bonham Carter declares the only way forward is to double down on commitment. "You have to go for it. You think, 'oh god, this is a ridiculous way of making a living,' but also fantastic too."

In the Alice in Wonderland sequel Alice Through the Looking Glass, the 49-year-old, London-born star gets to play on a stage best described as "the theatre of the absurd", assembled by director James Bobin using a style established by the original film's director, Tim Burton. And that environment – one part imagination, four parts cold, impersonal soundstage ringed by fabric curtain onto which the film's special effects team will matte the sets and effects – is not without its challenges.

"The room was f---ing awful, in all honesty," Bonham Carter says. Such directness is not unexpected. Bonham Carter has a reputation for her candour, and to meet her in person, in a jumbled hotel suite at LA's chic London Hotel, it makes a refreshing change from the usual film interviews in which an actor insists on crossing the marketing Ts and dotting the publicity Is.

In person, Bonham Carter is charming, a little guarded about her personal life but not so much that she doesn't flick through images on her iPhone. "That's my daughter, Nell," she says, proudly.

That Bonham Carter is a no-nonsense, speak-her-mind woman is hardly surprising. Dig a little into her family history and you discover she comes from a long line of no-nonsense, speak-their-mind women, perhaps most notably her grandmother, the politician and feminist Lady Asquith. The topic makes her smile with pride, but tinged with a little shyness.

In truth, she says, the generations of tough Bonham Carter women is not a topic on which she has dwelt for any length of time. "Ever since I was kind of well known it was something asked ... [but] I wasn't very conscious of it until I was 18 and was in the public eye," she says, adding: "All the women in our family are strong."

She adds that she also took a lot from her father, a merchant banker and "amazing man" who worked for the International Monetary Fund in Washington DC.

Despite a pragmatic quality to her family environment – her father a banker, her mother a psychotherapist – Bonham Carter says she grew up surrounded by fairytales. "Lewis Carroll has always been around me, I have always loved Wonderland and Alice and all the icons and the imagery and sort of ingredients of Wonderland, not necessarily the story but Alice herself," she says.

It would have seemed portentous that the director Tim Burton, to whom Bonham Carter was married, was asked to re-imagine the Alice in Wonderland story for the Disney studio in 2010. The first film offered Bonham Carter a chance to play the part of the Red Queen, a part so gloriously out of control it's not difficult to see why she leapt at the chance.

Bonham Carter had met Burton while filming Planet of the Apes. She then featured prominently in a number of his films, including Charlie and the Chocolate Factory and Sweeney Todd: The Demon Barber of Fleet Street. The pair had two children together – Billy and Nell – but in December 2014, announced that they had "separated amicably".

As a mother, Bonham Carter says she tried very hard to bring fairytales into the lives of her children. "The house is pretty fairytale-like," she says. "Nell's bedroom as a baby was a caravan stuck on the side of the house ... [and now] she has an attic room because I love Cinderella. It's all enchanting, but of course, she is such a pragmatist, she said, 'Come on Mum, I've started off life in a caravan and now I'm in an attic'."

Bonham Carter's performance brings an unexpected but powerful depth to Alice Through the Looking Glass. Unsurprising, perhaps, for an actress whose body of work is so varied, from The Wings of the Dove (1997) and The King's Speech (2010) to Bellatrix Lestrange in the Harry Potter series (2007–2011) and, more recently, the film remake of the American television classic Dark Shadows (2012), the musical Les Miserables (2012) and Cinderella (2015).

Her resume has one curious inclusion: the year she spent on the 1980s crime drama Miami Vice. Bringing up the topic elicits a wry smile from her. The devil is in the detail: what seems like a year in the annals of television history was actually filmed in not much more than a week, she says. "It was 10 days in Miami, it was fun, it was like completely being a fish out of water.

"A lot of things I did for fun. I feel sorry for journalists because they have to try and make some sense of it, but there is no sense. It's just random and a mess."

Setting aside the fast cars and white-seamed pantsuits of Miami Vice, there is little doubt that Bonham Carter is a considered actress. Each part seems to be chosen carefully, and each part, once accepted, is assembled in the most traditional of manners. In the case of the Red Queen, there are layers upon layers, small touches and large notes and, in some moments, even a bit of Carry On queen Barbara Windsor.

The mention of that last detail elicits a smile from Bonham Carter. "Oh, good," she says. "Yeah. There's a lot. I'm glad.

"I like the idea that there's a prism and other people pop out because that's what I do," she says. "I do go around stealing from people. There was a bit of Bette Davis, there was a bit of Gloria Swanson in Sunset Boulevard because she always ... there's a sense of narcissism and the need for attention."

In Alice Through The Looking Glass, Burton hands the director's baton to James Bobin. In one sense, Bobin inherits an established style book, so some of his choices are curtailed by the parameters laid down by Burton in the original. "He [Bobin] inherited a lot, obviously, but he made it his own. He's a really graceful man. He's a real gentleman, very clever, very creative.

"It's also focused on different characters. James had people like Sacha [Baron Cohen] with him as he had already worked with them. A bit like Tim and Johnny [Depp] have in that long relationship. It was really interesting to watch James and Sacha work together because they have that shorthand. They're certainly worth seeing, exhausting every possibility and inventing everything."

Of all the film's new elements, the most notable is Baron Cohen's Time, a half-clockwork, half-human master of the fourth dimension. Cohen's portrayal is unusually sensitive, even compelling. "I think it's his blue eyes," Bonham Carter says.

Baron Cohen is "totally unpredictable, like a hyperactive child sometimes," she says, quickly qualifying with: "I'm not saying that, I'm not."

She also had to be firm with her co-star. "He is very inventive, and he's fun, but ... I'm pretty direct with him. Sometimes I think what Sacha doesn't appreciate is that he's just telling a story. The weight isn't always on his shoulders. A lot of the time it's just playing the scene, not inventing the scene. He comes from such an improvisational background. He can't but help improvise. It's interesting."

Compounding the challenge: that pesky soundstage where it was shot. "There was not much atmosphere," she says. "You know the problem is this room is huge, and you see everything. It's generalised lighting, so there's no sense of focus, there's no sense of, 'OK we're imagining'.

"On most sets you realise where the drama is," she says. "What's in front of, what's the imagined reality and what's off, but here there was no demarcation between me and Sacha trying to work in, and seeing absolutely every other member of the crew basically bored out of their head, I don't blame them for playing Sudoku. It was hard because it was completely sterile."

In such moments, she reiterates, a deeper commitment is needed. In this case, to delve into the childhood of Iracebeth of Crims – the story's Red Queen – and rip open a Pandora's box of emotions. There is a festering wound from her childhood, Bonham Carter thinks, when her physical differences to those around her were made clear. "She wasn't broken I don't think, she was deeply hurt. I think that's what all bullies have. They've always got a great sense of insecurity and inferiority."

Alice Through the Looking Glass is now screening.