The following year, he embodied the poet aspect of Bob Dylan's life in Todd Haynes's I'm Not There. Now, inspired by the actor's "fragility", Jane Campion has cast Whishaw as the 19th century poet John Keats in Bright Star.
"Fragile" and "vulnerable" are descriptions that follow Whishaw around. In person, he is soft-spoken, slender framed, thoughtful and sensitive. But he admits that recently he has started to feel "there's a certain similarity between some of the characters I have played". He is "thrilled" parts have come his way, "but I realise now perhaps I am hungry for another kind of experience".
"It comes from getting a bit older," Whishaw concludes when we meet, a few days after he turned 29. "I'm changing, so I feel like I've got other things I might be able to bring to the table than just being young and sensitive, or whatever else people might think about me. As I'm getting closer to 30, I feel there's more to me than that."
Whishaw is not sure what this mysterious "more" is yet, or how it will express itself. But he senses it's there. "I'm curious as to what will happen," he says. "As an actor, you've only got yourself and the way you feel about things, and the way you look at things. And as that evolves and changes, inevitably your relationship to acting changes too and the kind of roles you might want to do."
Any development is bound to be worth watching. For though it is an overused phrase, in Whishaw's case it is no exaggeration to say that he is one of the most exciting and talented British actors of his generation.
In a relatively short space of time, he has accumulated the kind of notices that most actors can only dream about. When he played Hamlet in Trevor Nunn's production at the Old Vic, in 2004, aged just 23 (he had already essayed the role twice when he was 16), critics fell over themselves in praise of his performance. Nunn had wanted a vulnerable Hamlet and found a perfect match in Whishaw. "Great Hamlets blaze across the theatrical firmament about as often as Halley's Comet," wrote the Daily Telegraph, before declaring Whishaw one such great. "A Shakespearean star was born last night," concurred the Evening Standard. Some hailed him as the next Laurence Olivier – Whishaw winces when this is mentioned – which, while well meant, could crush some young actors. Did he feel burdened by the comparison at such a tender age? Apparently not.
"None of it feels real because it's just something written in a paper one day," he says. "We all know it really doesn't mean anything. The fact is you've got to find another job. And," he smiles, "you've actually got to do Hamlet every night. You get the review or whatever, but you've got another four months to do the performance, and you're just preoccupied with the doing of it? That's all I think about, really."
Praise is now being heaped on Whishaw's down-to-earth portrayal of Keats in Bright Star.
The actor's first proper love story, the film recounts the poet's blossoming romance with Fanny Brawne (winningly played by Australian Abbie Cornish), a young seamstress who lived next door to Keats on Hampstead Heath. Tragically, their relationship was cut short by Keats's untimely death in Rome, aged 25, the latest member of his family to succumb to tuberculosis.
Even though he loves poetry, Whishaw knew nothing about Keats before doing Bright Star; in fact, he was not a fan of the Romantics. "I had a bit of a prejudice," he says. Since we are sitting in a corner of the dimly lit bedroom of Keats' friend Charles Brown (played by Paul Schneider) in Keats House, Hampstead Heath, I fear we might be risking some supernatural intervention. "I just found the language too much," Whishaw continues. "Too syrupy, too rich, too luxurious. I liked Ted Hughes and stuff that's blunter and tougher."
Reading poems such as Ode to a Nightingale, though, he discovered a toughness and honesty he wasn't expecting. "It flies but is also connected to the earth," he explains. "That's a key feature for me." Indeed, he could be describing his own portrayal of Keats.
Part of Keats' tragedy was that his poetic genius was not recognised during his lifetime,In fact, he constantly came under attack from critics. Unable to earn a living from his writing, he was practically penniless, which, in the 19th century, did not make him ideal husband material in society's eyes.
In contrast Whishaw was just 15 when he won rave reviews for his performance as Primo Levi in a production of Levi's If This is a Man at the Edinburgh Festival – and the praise has kept coming since. Was it hard for him to grasp Keats' frustration?
"Yeah," he says, "but I think there's something to be said for not being recognised. When you're recognised, suddenly a whole load of other things come into play. I think I felt like that to a degree. You have a success with something and there's a sense, perhaps, that people want you to do the same thing again, or have an idea of what you should do next, or have an idea of that's what you do. And, actually, if you don't have any of that, you're in a beautiful kind of state of freedom just to create things."
Despite the savage criticism, Keats "seemed to have a sense of self-belief which is otherworldly," he says. "I don't know where it came from."
His willingness to tackle one of the pinnacles of the Shakespearean canon early in his career suggests that Whishaw isn't wanting in self-belief, either. Or was it just that he felt he didn't have anything to lose at the time?
"Well I think I have a degree of confidence but I also have terrible insecurity, like anybody does," he laughs. "But you need to have that because that's the thing that keeps you wanting to do it better, or to keep moving forward."
On the other hand, he didn't have anything to lose, he agrees, "and I think that is really important. It's something you've got to really fight to keep a sense of in yourself".
Bright Star finds Whishaw in top form again. But the film came towards the end of a string of projects, including the film version of Brideshead Revisited (in which he played Sebastian Flyte) and the harrowing TV prison drama, Criminal Justice, which left him feeling "really spent".
The weird thing about acting, he says, is that it "depends on being in touch with something that's childlike, because it's all about make believe. But you've also got to live in the real world sometimes, and I was finding it very confusing, because you realise you've had all these experiences – you've fallen in love, you've been to prison – but none of it's been real. I felt after that I had to do something that's actually real."
That said, he "mourned" leaving Keats' world behind. While loathe to romanticise it – Keats did die of TB, after all – Whishaw appreciated being in an era when people really connected with each other. "You weren't having these tiny text-message sized pieces of communication or grabbing a moment and then having to shoot off and see someone else, or communicating with someone through Facebook," he says. "You wouldn't see someone for months and months and then you saw them, and you'd spend time together. I think that's something that alarms me about the world we live in. It's so hard to fight for those moments to actually be with people."
Not that Whishaw is likely to have much free time on his hands for the foreseeable future. Having taken time off to recharge himself – one of the luxuries of being an actor, he says – he is back in full flow. He already has a performance in the can as Ariel, in Julie Taymor's screen version of Shakespeare's The Tempest (Helen Mirren plays Prospero, now Prospera), and will soon take to the stage in Cock, at London's Royal Court Theatre, before treading the boards alongside Hugh Dancy and Andrea Riseborough in an off-Broadway production of Alexi Kaye Campbell's Oliver-winning play The Pride.
There is no big masterplan, says Whishaw; he just wants to do good work, with good people. "The thing about acting is that it's fairly random. At the end of the day you take what drifts past you or what's given to you." He pauses for a moment. "I just feel very lucky to have worked, and to have worked with such wonderful people. I feel very blessed."
Bright Star is in cinemas from Friday. Cock is at the Royal Court Theatre, London, 13 November until 19 December.