Since she was plucked from teenage obscurity and thrust into the fashion premier league six years ago, Lily Cole’s iconic English beauty has had a peculiar effect on the world. Designers draw lipsticks at dawn to be the first to drape their garms over her. Teenage boys and married men get sweaty palms gawping at her Pirelli calendar and French Playboy cover. Housewives turn into green-eyed monsters watching TV adverts of her parading in front of Take That in M&S knickers. Charities clamour to get her to fight their corner. And her Cambridge lecturers have yet to mark her art history exams with anything less than a first.

Unlike other models whose popularity and looks are aligned to fleeting aesthetic trends, Lily transcends seasonal whims. Her alabaster skin, curly phoenix hair and woman-child allure have more in common with a John Currin painting or muse from the Renaissance than they do with the identikit age of Topshop. In her modelling career she has inspired Juergen Teller, Nick Knight, Craig McDean and Steven Meisel to push the boundaries of fashion photography firmly into the realm of the fantastical.

However, there is one part of Lily Cole’s life that hasn’t made hearts beat faster – her acting career. Save for an unchallenging bit part in the forgettable remake of St Trinian’s, Lily the actress has yet to cause a much of a ripple on Hollywood’s golden gene pool. And if the bitchier end of the blogosphere is anything to go by, there are many hoping that this quintessential young overachiever will sink without a trace.

The 21-year-old seems unfazed by any of the media hyperbole and speculation. Sitting in her hotel room at the Toronto film festival, she appears completely relaxed. Excited, even. After all, movie trade mag Variety recently praised her “thesping muscles” in RAGE, Sally Potter’s avant-garde fashion drama, in which she shares screen time with Dame Judi Dench and Jude Law.

But what most critics are getting animated about is Lily’s turn opposite the late Heath Ledger in Terry Gilliam’s latest flight of fancy, The Imaginarium of Doctor Parnassus. In it she plays Valentina, the 16-year-old daughter of Doctor Parnassus, a wizened old showman who makes a regrettable pact with the devil, trading her for immortality. She, in turn, yearns to escape from her life performing in his bizarre travelling theatre of lost souls.

Acting opposite veterans Christopher Plummer, Tom Waits, Jude Law, Johnny Depp and Colin Farrell, it is a role that pushes her mystique on to the next level. Wading gracefully through Gilliam’s hallucinogenic stream of consciousness without slipping up in front of such prestigious company, Lily proves once and for all that she is not merely a fashion chimera who gazes out of glossy paper windows. She has a screen presence that commands your attention, particularly in her scenes with Ledger. And, although his tragic overdose will forever cast a shadow over the production, it is Lily’s enchanting performance that everyone should be talking about.

Lily Cole: I don’t think I was intimidated by taking on the role of Valentina. It was only when I was doing a read-through with the other actors that the magnitude of it all hit me – the sheer amount of talent in the room really struck me. I was like, ‘Wow.’ I was intimidated for sure because I was new and relatively inexperienced. It was a deep swimming pool to be thrown in to. It was Terry’s belief in me that stopped me feeling nervous and we went from there.

Do you find it hard to avoid being typecast as the hot model?

I don’t think so. From Doctor Parnassus and RAGE, I’ve had nothing but positive praise, from what I’ve heard anyway, but I don’t tend to read articles. On my acting, people have been quite positive. There are plenty of pretty girls in the world, and Terry and Sally Potter would not have picked me if I could only contribute the physical aesthetic. Of course the physical aesthetic is important, but it would be narrow-minded to think that their choice of actors comes down just to that.

In RAGE you play a model called Lettuce Leaf. Was that your chance to have fun at the expense of the fashion industry?

No, not at all. Sally uses the fashion industry as a microcosm for her opinions on the world at large. She’s using fashion as a way to epitomise all of these ideas. She never made or intended it as a direct attack on fashion. The scenarios in RAGE are like nothing I’ve ever experienced in fashion, and the characters are from extremities that I have never witnessed. It’s all extreme, models are dying on the catwalk one after another, it’s slightly taken out of reality and is being used as a vehicle to discuss lots of other issues like globalisation.

Valentina is a world away from the fashion industry in RAGE. Was it hard for you to get into her mindset?

No, because they are both girls that are in situations I can relate to in some aspects and can imagine in some aspects. I don’t have that much more in common with a 14-year-old model discussing death as other models die around her than I do with a gypsy girl who escapes into her imagination. As characters they’re both familiar and unfamiliar, you know?

That’s an interesting question. Only on a very practical level. I obviously study and have friends that are my age, but on a practical level of flying around the world, or doing this interview or making more money than they do, those kind of differences do distinguish me. But I think that I have relationships that aren’t based on differences or careers, they’re just people that I find interesting, or lovely, or creative. I don’t feel alienated due to age or careers, I only feel alienated from people with different ideologies in life, and that’s not a product of my making.

Seeing as you’re a Cambridge art scholar, did you take Terry to task over his anarchic appropriation of Victorian art?

No! He’s very intelligent (laughs). We didn’t have to bounce off each other intellectually to enjoy one another’s company. But I’m sure the fact that I had been accepted into Cambridge gave him some peace of mind that I wasn’t, you know, dumb!

Do you find that your success as a model, actor and scholar endears or alienates people?

I’m not going to give up studying because I think that it might make people dislike me. If I make decisions based on what other people’s perceptions are of me then it’s going to be a disaster. It doesn’t seem like a sensible thing to do.

Critics are divided over Doctor Parnassus. The Times said that you were “mesmerising as the teenage siren”, but The Guardian called the film “an awful mess”. Why do you think Terry Gilliam’s films split opinions so passionately?

Terry doesn’t compromise. He could try and make it more commercially appealing to stop the polarisation, but his fans wouldn’t love his films like they do. They are extreme, crazy and visual and full of all these hundreds of ideas that he believes in. There’s always a lot to take on board. Some people love that and relish it, and some people don’t.

Everyone involved in the fi lm got a lot more emotionally involved in the situation. We started shooting about a month later and it was incredibly difficult, but it became less self-indulgent regarding my own struggles to finish the film and to play Valentina, and much more a collective thing because everyone was having a hard time with what happened. That collective momentum and love and respect between everyone made everything move forward.

Did his death make you more serious about acting?

No, Heath’s death didn’t make me more serious about acting, Heath’s life did. Putting aside him dying, which was horrible of course, from the very beginning my inspiration was getting to work with actors like Heath, Christopher Plummer, Tom Waits and Andrew Garfield, who are all so talented.

When you saw the finished film, was it hard to watch yourself and Heath having so much fun on screen?

It was a weird thing to watch, these six months of my life that were bizarre and emotional. To watch that over a few hours was a strange experience, coupled with watching myself on screen for two hours, which was an even stranger experience! Terry didn’t change the script, apart from a few things after Heath died. He didn’t change the shocking nature of Heath’s opening scene, or the line Johnny (Depp) says about dying young. It was quite hard to stomach given what happened, but I think that Terry didn’t want to change the story to appease the audience. He doesn’t compromise at all.

In the film, your father makes a deal with the devil in return for immortality. Would you ever make such a deal?

I don’t know. I guess with the career I’ve got, whether it’s acting or modelling or having to do an interview and talk about myself, there is a deal with the devil going on...

Lily, are you calling me Beelzebub?

(Laughs) No, but there’s a price to pay for putting yourself out at large to that extent. There are a lot of prices to pay, and I guess some of them I’m not even aware of. At the same time there are a lot of reasons to do it. Every choice in life is going to have its pros and cons. This is all just an extreme version.

Do you think that your performance in The Imaginarium of Doctor Parnassus will surprise people?

I have no idea. I would hope so but I don’t want to put any expectations on it. I feel lucky to have had this experience.