Good golly, Miss Molly

Her first major role was as a necrophiliac in Kissed, and Molly Parker's next two films are no less provocative. Fiona Morrow asks the new queen of the indies exactly where she draws the line

"I'm just going to hold it, if you don't mind." Molly Parker clutches a cold bottle of mineral water to her chest like a baby and sighs with pleasure.

It is one of London's sweltering blasts of a day, and Parker, presumably having expected a more benign British summer, is suffering. Yet despite being overdressed in a thick, ruched cotton shirt and heavy ankle-length denim skirt, she projects absolute coolness.

Though more people here are likely to have seen her playing the heavily pregnant Molly in Michael Winterbottom's magical Wonderland, Parker's first major cinematic role was as the necrophiliac Sandra in Lynne Stopkewich's debut, Kissed (surprisingly sweet considering we witness trainee mortician Sandra exploring her desires to the full).

Parker's next two films to be released here are no less provocative: Stopkewich's second feature, Suspicious River, and Center of the World, Wayne Wang's explicit foray into sexual fantasy.

Both films are, to a certain extent, explorations of detachment, studies of the gap between the emotional and the physical. In Suspicious River, Leila (Parker) is a woman so completely cut off from her feelings that she degrades herself further and further sexually until finally she comes up against a pain strong enough to shake her. While as Florence, in Center of the World, Parker plays a lap dancer forced to face up to the personal compromises of her professional rationale.

Her performances have, I suggest, built an attention-grabbing CV, but Parker demurs with a shake of her head. She draws calmly on a newly lit cigarette, thinking carefully before responding: "I think, naively perhaps, that I don't look at things that way."

She speaks slowly and clearly, with a slight crispness around the edges of her Canadian twang.

"I remember maybe having one brief conversation with my agent about Kissed, saying it's a bit out there, but honestly, my grandest hopes for that film were that some other film-makers might see it and want to hire me."

Though she had only been acting for a few years at that point, Parker says she was ready to quit: "I was desperate to stop doing trashy TV – the writing was so bad and it was just all so compromising."

What is important, she says, is that the work is interesting, that the characters are intelligently drawn. I make a jokey reference to Hollywood, yet to embrace her talents: don't all actresses secretly want to be Julia Roberts? She looks at me, aghast: "Oh, I don't think that's true at all."

Still, despite being desperate for serious work, Parker does admit she thought twice about taking on Suspicious River: "I was reticent about the material – it was so dark – and just in a self-preservation way."

She wrinkles her nose and physically shudders. "Ugh, the idea of going there was exhausting to think about."

She had responded badly to a first draft, and was brought round through reading the novel on which it was based: "It is incredibly poetic and disturbing, but beautiful. And I was really engaged with this ability to disassociate from one's body."

Asked what preparation she makes for such roles, Parker smiles as she responds quickly: "There's not a lot of research you can do about being a necrophile," before adding, more thoughtfully, "I think it comes in stages. I usually approach the work initially from an intellectual place of trying to understand and make choices, and then the doing of it is much more instinctual and much less in my head."

Her job, she insists, ends when the shooting stops: "I am fairly able to let it go, until I have to do this stuff, where there's always this odd..." She hesitates, takes another long pull on her fag, though the smoke appears to evaporate in the face of her almost ethereal cleanness, and changes tack: "I do believe actors have a responsibility. I mean, specifically as a woman, I try to be conscious of representations of women in film, so you always hope that nobody fucks that up."

Working on films with sexual themes makes her especially vigilant: "I've never done a nude scene in any film that I felt hasn't been honest or has been there just to titillate. And I'm always on it with the director about 'Why?' 'Whose gaze is this?' 'What's the point of view?' 'What are you really saying with this material?'"

So how did it feel watching The Center of the World and seeing her character totally objectified by the male gaze, constantly spread across the screen as the most predictable sexual fantasy imaginable?

Parker meets my gaze with an even stare: "Yeah, well, it's a man making a film. Wayne [Wang] is always going to identify more clearly with the male character." But she's either naked, dressed as a fetish, or being sucked and screwed in almost every scene, while Peter Sarsgaard, who plays the fantasist, shows us his backside once or twice. "I agree,' she answers. "Some of that is a little bit problematic for me." She lets out a long sigh, something like the steam from a pressure cooker being very carefully released.

"But it's really hard to have any control over that. On the day when you're there, you can do everything you can to point it in the direction that you feel comfortable with, and after that it's just not up to you. That's when it gets harder to make decisions about what to do and what not to do. And I guess if you don't think the movie works, then it ends up looking like a bad choice."

And where does she draw the line? Could she imagine taking things as far as Kerry Fox did in Intimacy – the current benchmark for on-screen sex?

"That's a big leap," she says, pushing her hair back from her softly freckled face and frowning. "It was brave of her and I don't know if I could do that. Frankly, I think The Center of the World could have gone to that place and I..."

There's a long pause, before she continues, irritation creeping into her voice: "I wasn't willing to do that." She frowns again, then adds quickly and slightly crossly: "It just wasn't necessary in this film."

Maybe it's just too hot, or maybe it's one criticism too far, but I sense Parker's patience snap when I move on to my problems with Suspicious River and the character of Leila – as dreary an example of woman-as-eternal victim as you're likely to see.

"Yeah," she challenges, "but they are out there and it does happen. It's a movie about self-destruction, and if she is victimised, she makes choices to be so. She engages in a very abusive relationship that brings her back into her body and she knows that there is something in there that she needs to find even if it takes her to her death."

Possibly I look a little blank. "I can tell you're bothered by something," says Parker quickly, "I just don't know what it is."

Before I can respond, she jumps back in: "There's this idea – and I don't really understand it or buy into it – that it's more brave to take this kind of role, but it's just not as big a deal to me as it seems to be to a lot of people. I think," she continues, looking pointedly at me, "it's misplaced and based on their own morality and their own ideas of what must be difficult, and often they are difficult but not for the reasons that one would assume."

We have reached an impasse. She sits bolt upright, her increasingly emphatic smoking the only visible sign of her palpable frustration. I'm no actress, so my response is to pull at my hair and screw up my face.

This failure to connect is doubly disappointing because I had such high hopes. Parker's one of the brightest, most intriguing talents bubbling just beneath a major breakthrough. Yet she is totally taken aback by my questions and I'm frankly baffled as to why she wouldn't expect them.

She leans forward to dispose of her dog-end. "David Mamet talks about..." she begins, before tapering off with a bored shrug.

"Anyway," she concludes, "it doesn't even matter."

'Suspicious River' is released on 31 August, 'The Centre of the World' on 21 September