So I'm not surprised that even when he tells me how he deals with paparazzi trailing him with his children, a subject that clearly upsets him, his own account of getting angry seems more like a Sunday school lesson in forbearance. "There have been three or four occasions – the guys in Australia, particularly, are very sensitive, at one level they do understand – where I've said 'OK, you have to do your thing but please don't let my kid see you doing it'," he says. " 'Please do your job better; just hide better. I don't want him to see.' And most of them do that."

The role that has ostensibly earned him most of that unwanted tabloid attention is Wolverine, the hirsute, clawed and dazzlingly muscled mutant from the comic-book adaptation X-Men, its sequels and spinoffs, with a new "origins" flick, The Wolverine, coming out next year. Being a man with steel paws is not usually a route to magazine-cover celebrity. But neither is being the best thing in an indifferent film, as Jackman so often is.

Look at the film credits he's amassed since cracking Hollywood in X-Men. There have been modest performances in films such as The Pre-stige, Deception, Woody Allen's vapid Scoop, and the recent Real Steel (described by one critic as "the world's first and possibly last touchy-feely boxing robots movie"). Then there is the extravagant flop The Fountain, and Baz Luhrmann's silly, bloated Australia. But it doesn't matter: he has still been asked to host the Oscars and dubbed "the Sexiest Man Alive" by People magazine.

When I meet him, Jackman is rejoicing in having just had four days when he didn't have to sing. X-Men fans probably don't know it, but Jackman made his name in musicals; his leap from small Australian features and television series to the international stage came in 1998 with Oklahoma! in London, where director Trevor Nunn dared cast this Australian unknown as Curly and unleashed a new leading man in the process. In 2004, he won a Tony for his hit run of The Boy from Oz on Broadway. Late last year he had an even bigger hit with a one-man show of songs and stories. "I've been amazed at my career," he says cheerfully. "I constantly feel blessed to have got what I've got. I kept saying, 'If I could just do this for five years and make a living, that would be great'."

For months now, Jackman has been working on Les Miserables, the much-touted blockbuster adaptation of Schoenberg and Boublil's hit musical, in which he leads a cast including Russell Crowe, Anne Hathaway and Amanda Seyfried. He has been singing for 10 to 12 hours a day because the director, Tom Hooper of The King's Speech fame, insists that everything be live. Tough, he agrees. "Like it should be. I mean, I'm playing Jean Valjean, which is like the King Lear of musicals. The span of his life, the songs, the range of the singing – it's about a 2½-octave range – in every way, it pushes everyone to their limit.

"I think it's something to do with the nature of the material. It's about people under duress, at breaking point, and how people handle it. Ultimately, it is very elevating – it's about the human spirit. So it should be like that."

The Easter Bunny in Rise of the Guardians was clearly not difficult, especially as he had the unusual luxury of speaking in an exaggerated version of his own accent. Rise of the Guardians is a kind of The Avengers for smaller children, in which the defenders of goodness – Santa Claus (called North, made into a huge Russian with tattoos and voiced by Alec Baldwin), the Tooth Fairy (Isla Fisher), the Sandman, Jack Frost and the Bunny – join forces to defeat the fearsome Boogie Man (Jude Law, renamed Pitch). Why the writers decided to make the Easter Bunny Australian is something of a puzzle – I kept expecting the CSIRO to appear with a Santa sack of the poison 1080 – but as far as Jackman knows, the die was cast before he was.

"I saw the picture of him with the boomerang and a kind of very proud stance and I loved the idea of him being into nature as the herald of spring," he says. "That's all about the natural order of things; the idea of nature protecting children, but also children protecting nature. I have two children and it's amazing how in tune they are with nature, with light, with smells, with time. Easter Bunny is like the protector of that, and I loved that side of it beyond the religious side of Easter, which I grew up with."

Jackman had a solidly Christian upbringing in Sydney, the youngest of five. His parents had emigrated from Britain; when he was eight, his mother abandoned the family overnight and went back to England. His two sisters later joined her. His father, whom he clearly reveres, brought up the three boys. The boogieman was just one of young Hugh's many terrors; one of his brothers was able to terrorise him for a month, he remembers, by lying under his bed tapping on the springs while he was too scared to take a peek at whatever was underneath him.

"I was quite a fearful child, actually. I remember being afraid of even going into the house. I used to often be the first one home from school and I often used to wait outside." Once in, he would immediately switch on a radio for company. Even at 14, he was afraid of the dark; a night alone in the bush on a school survival camp proved the brutal cure.

He thinks he was about eight – when his mother left, I notice – when he spotted his father laying Christmas stockings at the children's heads when they were all crammed into a tent on Christmas Eve. The next day, Christopher Jackman clearly felt forced to explain there was no Santa Claus. "I'd actually either forgotten or just didn't twig what he was doing, but the next day he told me and I was just devastated; I was bawling my eyes out. I'll never forget it. It was raining, so we were all inside the tent – that's the moment when camping holidays are the worst: five kids sitting inside a tent and my father trying to cook on a little stove – and he's telling me there's no Santa."

A frightened, motherless boy: it isn't easy to square this picture with the ebullient grown-up Jackman. He has since been reunited with his mother and recently said he recognised she suffered debilitating post-natal depression and "struggled" with parenthood. "There comes a certain point in life when you have to stop blaming other people for how you feel or the misfortunes in your life," he told The Australian Women's Weekly. Anyway, like all good parents, he is only too aware of his own shortcomings. He and his wife, Deborra-lee Furness, have two adopted children.

Maximilian, 12, asks Jackman daily to quit acting. "He quite likes it when I do my one-man show and he has been on stage a few times to play the didgeridoo, for which I was very proud of him because he's a little shy. But just yesterday,  we were walking and there were eight paparazzi outside and he says to me, 'It's your job, I hate your job!'"

What about his daughter? Ava is seven. "That worries me more, because I think she kind of likes it. Seriously. Sometimes we'll come out and I'll see the paparazzi and say, 'OK, left' and at one point she said, 'But dad, the paparazzi are up the other way!' That one is going to be asking me to get her an agent when she's about 11." He snorts with laughter.

So what about him? Is there a part of him that likes to be the centre of attention? He considers the question, as he always does, with care.

"Hmm. Well, we're going to get into some kind of therapy here, but I always love that quote from Bono. He said, 'What kind of hole must there be in my heart that requires 70,000 people to chant "I love you, Bono" simultaneously, just to make me feel good?'" He laughs. "And I think that of course there is some dysfunction of needing to be liked or noticed or to feel part of things, something going on there for most actors. For some there's not, and I think they really struggle with it. Me, I'm sure there's a bit of a ham, a show-off in there. But I don't know. I don't think of myself in that way, but I'm sure there's something going on."

And true to form, he's nice enough to admit it.

Rise of the Guardians opens December 13.