Six months ago, Ewan McGregor strolled incognito down the Croisette at the tail end of the Cannes film festival. He was dressed in bright white, with a beard, shades and a wide-brimmed hat pulled down to the eyebrows. In the hubbub of the Cote D'Azur's garishly dressed, he somehow melted into the crowd. Intent, or accident? "I wasn't in disguise," he says, taking slight umbrage at the suggestion. "I'd just been given a really nice hat. So I thought I'd wear it. I think if you put a cap and a pair of shades on in an airport, of course everyone's gonna look at you. But I'm not worried about it. I don't feel like it's a curse. If you're gonna be on TV and film, and expect people to watch you, of course they're gonna look at you in the street. What else would they do?"

McGregor has been in the business nearly 20 years, and in that time he has segued smoothly from a rebel hero of new British cinema – epitomised by his turn as junkie pin-up in Danny Boyle's Trainspotting – into a suave leading man, the latter cemented by his recent (surprise) Golden Globe nomination for Lasse Hallström's fusty romantic drama Salmon Fishing in the Yemen. Until 10 years ago his penchant for full-frontal nudity – The Pillow Book (1996), Velvet Goldmine (1998) and Young Adam (2003) – threatened to overshadow any genuine acting talent but, with his performance in The Impossible, he has put all that behind him.

The Impossible is the second film by Spanish director Juan Antonio "Jota" Bayona, who caused a stir with his first, The Orphanage. Where The Orphanage dealt with the mysteries of the supernatural, The Impossible deals with the miracles of the real, telling the story of a married couple (McGregor and Naomi Watts) who go on holiday to Thailand and get caught up in the horrors of the tsunami that hit the country on Boxing Day 2004. McGregor gives a wonderful, low-key performance. One that truly serves the core, intimate drama of a film that, like Nicolas Roeg's Walkabout, isn't just an account of what happened but is also about the psychological aftermath. The trauma and the tragedy is replicated with incredible realism. A standing ovation greeted its premiere in Toronto, where we meet; it's now considered a good bet for a best picture Oscar nomination. Even the mere script, says McGregor, was devastating. "What you got from it was the brutality and truth of the story, through the eyes of that family. In terms of scale, though, it's all very well to read that your character is walking through a devastated area. But it's not until you get on the set that you think: Oh my God …"

He says this because, although many of the special effects were reproduced for real – being cheaper than CGI – in a studio tank in Alicante, much of the shoot took place on location, on beaches still scarred by the tragedy. "It was a very difficult film to make," he says, "especially with the weather. We had a lot of rain, and the actual day of the original tsunami was very beautiful, so we had to wait. There was some talk among the Thai crew that the film might be …" – he pauses – "… cursed, you know? That the spirits or the gods might be preventing us from making the film." He pauses again. "There were some spooky moments."

So spooky that the crew held a ritual to "appease" these spirits, sending lanterns up into the skies. As soon as they did so, the wind sent them flying in every possible direction. In retrospect, it probably wasn't so much a warning as a reminder of the unimaginable chaos of that day. Says McGregor: "Jota has always said – and he's right – that crying was a real privilege in that situation, because nobody had time. And so when people did cry, they totally fell apart."

McGregor is 41 now, and The Impossible is one of his best performances. It requires him to be loving, thoughtful, anxious, scared, bold and broken without the prop of a genre script where the bad guy will be brought to book and right will prevail. Because, although there is heroism, this is not a story about heroes. "I guess it's my first 'dad', really," McGregor says brightly. "I mean, I've been a dad in … Well, I think – because I can't remember – that in Nanny McPhee 2 I had kids."

He racks his brains. "Nothing springs to mind. Anyway, I've certainly never made a film that felt to me like an exploration of that, of what it means to be a parent and that love you have for your kids. This was that for me. This is something I've been experiencing for 16 years of my life, and it's not in my work really anywhere. I thought – albeit a really extreme version of that – it was a nice way to look at that specific and unique love you have for your kids."

Which is interesting in itself. For female actors, the leap from ingenue to mother roles is an occupational hazard, and one to be avoided. McGregor acknowledges the double standard. "The first time I remember anything like that was on the last film I did with Naomi – Stay [in 2005], with Ryan Gosling," he says. "One day on set I suddenly realised I was the doctor. And I went, 'Oh God … He's the young guy – I'm in the suit! Fuck!'"

He laughs. "But that was a long time ago, so it's been happening for a while."

Did he ever dread that day? "No. I didn't really. Not at all. I mean, I was somewhat surprised it didn't happen earlier, because, like I said, I've been a dad for so long. I really like kids."

And he must do, being a father of four ("All girls," he smiles).

Which seems a far cry from being the British film industry's great white sex symbol, the guy who should crash and burn, not live happily ever after. But McGregor seems content enough. He's still a very handsome man; his hair spikes up at wild angles, and there's a lovely glint in his eye, especially when he smiles. He's strikingly unguarded, too; at one point blurting out the title of his next project.

"Please don't mention it!" he pleads. "I totally forgot. It's funny; you do sort of lose your marbles. I was sitting here, and somebody went: 'What are you doing next?' And you're brought up up to answer questions, so I said: 'Oh … !' But I was told yesterday: 'Don't mention it! Well, not just yet."

Is he comfortable doing press? "It gets better, I think, because it gets easier. It's more difficult when you're younger, somehow. Maybe there's less to talk about." He sighs. "It's not great fun sitting in a TV junket all day. It's not. But this kind of thing is fine, having a chat with somebody. I always feel like saying to people: 'Just enjoy it more. Don't worry about it.'"

Is that a result of coaching? "I never had media training, because I'd been doing it for years. I remember the first ever interview I did. Oh fuck, it was in Salisbury Playhouse, and I had to do an interview with TV Quick for Lipstick on your Collar, which was coming out soon. I remember doing it on the phone in a broom cupboard, because I was so embarrassed. My big moment! I didn't know what to do. I probably talked too much. But I always think that you may as well say what you mean, or there's not much point in doing it, really. There are areas I won't talk about and don't feel that it's relevant to talk about. But not many. Not many."

The next time we meet, McGregor is in London for the film's UK premiere. Two months have passed, and the glint in his eye has dimmed a little after a day in Claridges being asked about death and disaster. The film has been a huge hit in Spain, but the backlash has kicked in, with some reviewers questioning the director's decision to focus on a western family (the original family were Spanish) and sideline the Thai people's experience.

McGregor isn't surprised. "It's a very easy and not very clever criticism, I think," he shrugs. "Because the truth is, it's a story about this family, this western family, who are on holiday there. And that story is many, many people's story. But to say that it doesn't tell the Thai people's stories …" He sighs. "Naomi's character is saved by a Thai man, and taken to safety in a Thai village where the Thai women dress her. It's one of the most moving scenes in the film, really. In the hospital they're all Thai nurses and Thai doctors – you see nothing but Thai people saving lives and helping. Most of the survivors we spoke to had nothing but amazing things to say about the Thai response to the tsunami, in that they mobilised themselves very quickly.

"I think it's criticism for the sake of criticising, in a way. People said that about Black Hawk Down: 'Well, it's just the American story.' Well, yeah! It was a film about the American side of the story. So that's what you do! You tell a story. And we were telling this family's story."

In the meantime, he can finally discuss the film he let slip in Toronto, August: Osage County, directed by West Wing producer John Wells and adapted by Pulitzer prize-winning Tracy Letts from his play. "Boy did I have a good time on that one," McGregor grins. "We just finished it, Friday night. Eight-week shoot. We had an amazing cast. And I had a front-row seat to watch Meryl Streep."

Then there's the small matter of Star Wars, and the return of the franchise. "They let me know the night before they announced it," he says. "Which was nice. I got an email from them, so that I'd be prepared. Other than that, I don't know anything about it. But if they need me to be Obi Wan Kenobi again, I'd be delighted to do so, yeah."

Where other actors might be dismissive, or jaded about returning to such an iconic role, McGregor seems genuinely enthused by the prospect. Does he still get excited by going back to work?

"Yes," he says. "It's such an adventure, every time you go. It's such a great experience. The downside is that it takes you away from your family, and with kids who are in school, it does. There's no two ways about it. I used to be able to travel with them when they were tiny, but I can't do that now. And they're so spread out in age that it would be impossible. That's the downside. But the upside is that you get these incredible adventures. I'm always excited about them. And you can be disappointed. They're not all great experiences. Some films are much harder work than others, some feel like a holiday. But each one is unique."

• The Impossible is released in the UK on 1 January 2013