You wouldn't blame Naomi Watts for feeling the pressure. Presenting yourself to the British public as Princess Diana must be a little like meeting the stroppy teenage children of the widower to whom you've just become engaged. Whatever you say or do is bound to be wrong. Those who thought the Princess a flake will accuse you of hagiography. Those who loved her will suggest that jigs are being danced on her grave.

Earlier this morning, Watts may – or may not – have made an early exit from an interview with (the usually emollient) Simon Mayo for BBC Radio 5 Live. The recording allows the possibility that she may have felt somebody was trying to wind up the interview. It's all a bit messy. But it certainly sounded as if she was in a tense place.

A few hours later, having ensured that Oliver Hirschbiegel, director of the much-chewed-over Diana, sits in quietly on our interview, Watts seems confident, good-humoured and largely free of shellshock.

True, she has been in and around showbusiness all her life. Born in Kent, raised in England and Wales until her parents left for Australia when she was a teenager, Naomi Watts is the daughter of Myfanwy Edwards, a costume designer, and Peter Watts, a road manager and engineer for Pink Floyd. (That's him laughing crazily on Dark Side of the Moon, trivia fans.) But she can never have been under this sort of pressure.

“Yes. That’s fair. It’s a lot,” she says impressively calmly. “Yeah. I’m looking forward to next month. It’s a lot of pressure. Fifteen, 16 years on and we’re still obsessed by her – both royalists and anti-monarchists. She commanded attention. And maybe her death added to that. It added to that love people felt for her. Her life was way too short and we’re not comfortable with that. We don’t understand it.”

Whatever you felt about Diana, you couldn't deny that – like the weather – she was a constant, unavoidable presence for nearly 20 years. Or maybe that was different for Watts. It's a funny thing. We think of her as being every bit as Australian as her great pal Nicole Kidman (who was born in Hawaii, come to think of it). But Watts was half grown-up when she left the UK.

“I can tell you exactly where I was for the two big events in her life: her wedding and her death,” she muses. “The events in between are trickier. I left England when I was 14. I wasn’t reading the newspapers. But I was obviously aware of her. In Australia, she was definitely in the news, but not enough for me to obsessively follow her day-to-day movements. My opinion of her was that she was definitely a fascinating woman. She generated a lot of intrigue for a reason.”

Hirschbiegel's film focuses on a relationship between the Princess and Hasnat Khan, a heart surgeon, which is alleged to have begun two years before her death in 1997. Watts doesn't deliver an exact copy of the woman we remember from every news bulletin. Taking on the structure of a romantic comedy, the movie allows Diana to pine, stalk and flirt like a relatively normal society girl. One wonders to what extent Watts set out to create a character and to what extent she was fenced in by the legend.

“I’m interested in showing more than one colour with every character I take on,” she says. “I think there was a lot of room to move around with her. She was someone who did a lot of extraordinary things. But, in that process, she was trying to be as ordinary as possible. This film is focused on the love story in that two-year period, a time when she has broken away from the royal family.”

Is it Watts’s view that Diana was trying to reinvent herself? Was she trying to create a new personality for herself?

“Yes. That’s exactly what she did. But that was difficult because she was under constant scrutiny. Spontaneity required planning. She had to protect herself as much as possible.”

There is an undeniable spookiness to those scenes that touch on familiar footage and familiar snatches of (this is surely the right word) dialogue. The interview with Martin Bashir particularly stands out. "There were three of us in this marriage" is as familiar a phrase – if a little less weighty – than "Ich bin ein Berliner" or "One small step for man".

“It was spooky,” Watts says. “Particularly that Bashir interview. That was one thing that I wanted to get exactly right. Not just what she said, but how she phrased her lines, when she took breaths, when she touched her face.”

So a lot of study went on? She looked closely at Diana the performer?

“Yes. There were moments when I was saturated in the material, saturated in study. The Bashir interview became like my favourite book on tape. I played it constantly. We remember all those details so well. I needed to be as accurate as possible.”

What a strange place Naomi Watts now finds herself in. Even for a two-time Oscar nominee, this is an entirely different class of attention. Maybe it helps that she took quite a while to achieve proper stardom. Following her dad’s death from a heroin overdose in 1976, she moved with her mother to Anglesea.

Eight years later, she was on the other side of the world. She did a bit of modelling in Australia. She appeared in the odd commercial and Home and Away. But it wasn't until 2001, when she starred in David Lynch's Mulholland Drive that Hollywood really started to take notice. By that stage, Watts seemed to have turned herself into an undiluted Aussie.

“There’s a long and confusing answer to that,” she says. “I think I’m English. That’s probably because my mum and dad are English. My grandmother was Australian. The rest of the family were Welsh. And I lived in Wales for three years. That’s a third thing to add to the identity crisis. America is actually where I’ve spent most of my life at this point. So it’s such a long-winded story.”

At any rate, she soon made up for lost time. A slight woman with a surprising capacity for sudden intensity, she has managed to work with an impressive array of great directors: Woody Allen (on You Will Meet a Tall Dark Stranger), Michael Haneke (on Funny Games) and, of course, the impenetrable Mr Lynch himself.

“I love directors,” she nearly gushes. “I can’t bear it when a director doesn’t want to direct me. I can’t bear it when they leave you be. A lot of actors are the opposite. A lot of actors gets prickly about being told what to do. They’re like: ‘Yeah, yeah, got it.’ Not me. I love getting notes. I love getting a new idea for every take.”

In recent years, Watts has made a habit of playing real people. She was very good as Helen Gandy, assistant to Leonardo DiCaprio's J Edgar Hoover in Clint Eastwood's somewhat underrated J Edgar. She was Valerie Plame Wilson in Fair Game. She received her second Oscar nomination for playing Maria Bennett, survivor of the Indian Ocean tsunami, in The Impossible. That, she says, was a great responsibility.

“In Maria’s case – although she lived, hundreds of thousands of other people didn’t, so you’re telling a story for all the people who lost people,” nods Watts. “There is a huge amount of responsibility. In the case of Diana, everybody around the world knows who she is and what she did. So there’s a recognition there that needs to be honoured. And then there are the Princes. We really do need to be sensitive toward them as well.”

She seems to have some understanding of the media mudslide that’s about to come her way. That complicated geographical timeline must help. She’s both an insider and an outsider.

“The British are a poised, measured people,” she says. “They’re not like the Americans. They’re not demonstrative. I think they were surprised by their own grief for Diana. They were surprised that – as a collective – they felt the need to grieve. It’s obviously a lot to do with who she was. That explains why an entire nation came together.”

Still, today’s events suggest that Watts is still a little spooked by the current situation. She did suggest earlier that she was looking forward to it all being over. I can’t say I blame the poor woman.

“I am a little bit scared by it. I was scared by the passion that the project inspired. But that’s part of the job isn’t it? Isn’t it?”

I suppose it is.