I don't think Matt Smith has an unenthusiastic bone in his body. True, he has a nastily damaged and very specific one, in his back, which cut short a proper professional football career, but even that one's still probably enthusiastic. He and his bones exude not a hint of a slump of possible ennui, ever, for any aspect of his own life or, winningly, anyone else's.

He really is like Tigger. I suspect had I met him a couple of weeks after this joyous Indian-summer morning, after his reported split with model Daisy Lowe, there might have been a certain underlying… subduedness. Breaking up is, I think they say, always hard to do. But I'm truly not sure; I don't know if those bones do subdued.

He lollops in shedding croissant crumbs and apologies for lateness and resolutely failing to blink at the sight of two grown and outwardly pleasant men, Murdo the photographer and his assistant, steadfastly smashing the bejesus out of a television – as the 11th and youngest incarnation of the Doctor, he's seen much, much stranger. Within five minutes of our meeting he has broken off the interview to ask, honestly intrigued, about what passes for my shorthand and how it all works. At one stage an offshoot of the conversation somehow reaches five full minutes on the Higgs boson, and later, discussing Harris Tweed – when I tell him the crofters used to strengthen it by steeping it in something named, with a stoic Hebridean lack of euphemism, the "piss bucket" – he almost leaps to his feet with excitement.

Perhaps he was the best pupil ever, a decade ago. Or perhaps at 29, that good age for genuine inquiry, having garnered critical appreciation for managing the near-impossible and not being in any way a disappointing follow-on to David Tennant – with a legion of fans, a hot new assistant in Karen Gillan and, back then at least, an extremely pretty semi-famous girlfriend, and talent, and knowledge, and plans – he's simply that lucky thing: a man with the world at his feet and wanting to find out more of it every day. It is all rather refreshing.

In two days he flies to Los Angeles to collect an award – "Best sci-fi actor, who'd have thought that?"; the trip comes less than a week after the faintly different environs of Cardiff, where he's just finished shooting the Doctor Who Christmas Special. "It was a really tough shoot," he says. Enthusiastically. "Out in a forest, at night, and because there were children involved, some shooting schedules had to change radically, we'd often have to shoot through, no breaks – you get lunch at midnight or something. But worth it, certainly: I think it'll be a great show."

I had understood, before, that his love life and the Christmas special were essentially off-limits, so decided to ask him directly about both; he laughs generously and is far from guarded. "Well, the show. OK. It focuses around the Doctor meeting a family, in particular two young children, and their mother, played by Claire Skinner, and of course they enter a world which perhaps they shouldn't have entered, in good faith, and… well, a jolly old time of it. Around the Second World War. I've got huge hopes for it; the director Farren Blackburn, who just did The Fades [BBC3's apocalyptic teen drama], has given it great scale and colours – it's almost Tim Burton-esque. It's quite strange because I go away and do other jobs and then come back to this and, honestly, there's really nothing quite like playing the Doctor."

He's had two years, now, to inhabit one of TV's most famous characters. Does he feel he's changed him at all? "I don't wish to avoid the question, honestly, but it's a kind of hard thing isn't it, commenting on your own work? I think I'll probably have a more definitive – at least a more interesting – answer to that in the future. I don't want to be too conscious about that because I'm still in the middle of that, it's still evolving. From year to year."

And century to century. "Absolutely. As the doctor ages he gets younger and sillier. He's over 1,000 now, I think. And – oh, I just like him. His lack of cynicism. He's like a baby. He wants to sniff, to taste, everything; he'll never dismiss anything. As we get older – perhaps I'm just speaking for myself – we can get too cynical. If he had a… bath, it would be filled with rubber ducks which could talk or something; he'd find a way to reinvent the common bath. And I admire that."

Does Smith, I wonder, worry about being identified too much in the future with this one character, delightful as he is? "I don't, really. Any actor worth his salt has a responsibility to reinvent himself from part to part. Perhaps there'll be a period of carryover, but I'll take myself off to theatre for a year, or write, or direct, or – actually I might be directing something soon, in December – I can't say too much yet, but if all goes to plan, it's with a writer called Simon Stephens, who's great, but it might not come off so I don't want to say too much. But hopefully the work I do after coming off the Doctor will be of a different… tone."

Stephens is artistic associate at the Lyric Hammersmith and an Olivier winner, and I remember being shockingly moved by his Sea Wall in Edinburgh a couple of years ago, and thus I sense Mr Smith does want, soonish, to get… serious. Does that mean his doctor's incarnation is now measurably finite? Three years? Five years?

"It depends on your physical and mental state at the end of every shoot. I just take it year by year, but I'm quite excited by the coming year – it's the 50th anniversary, which'll let us be even bigger and bolder than ever." It's harder to think how much bigger, bolder, stranger. Don't there come limits? "Never. Not in Doctor Who. That's the beauty of it. You're never bound by logic, or time, or genre, or space, or location, which is what makes it such an ingenious televisual conceit."

I hesitate to ask because there are so many, many fans – myself included most of the time – but the last series was criticised for being too complicated. Did Matt ever think the scripts were veering towards being a bit… silly?

"Absolutely not, no way. By its very conceit – you've got a 1,000-year-old alien that looks like a human with two hearts who travels round in an impossibly dimensioned box – there's no room for it to become too silly. Why, do you think it's too silly? You don't look like a man who would find Doctor Who silly!" No, I don't really, and surely there are parallels with Douglas Adams – one of the early Who writers – who later, in Hitchhiker's, created a universe to explore not science fiction but the human condition. "Well, quite. The genre is a great way to write yourself out of any corner, certainly, which helps – but it also places human drama, relationships, right at the centre, which is what I think we invest in, and by human I include the doctor."

This Christmas the Doctor won't be the only Special on the block – it will face a fearsome challenge from Downton Abbey. "I've never seen an episode," says Smith, "but I'm good friends with Hugh [Bonneville]. My mum loves it and it's been doing brilliantly – but I'm just not interested in ratings. Overnight ratings are dead. It's just not the way TV is sold any more." He will be watching with his parents, about whom he talks much and happily, in Northampton. It was when younger, here, that a series of nasty back injuries ruined what was a promising football career and led accidentally to this career.

"I'd been playing football my whole life, really. Loved it – still do. I was at Leicester City at the time, and it wasn't any one incident, just a succession, and it was L5, my lumbar 5, there was a problem with that. I'll never forget it, the day before my history GCSE, and Leicester said they wouldn't be extending my contract because of it – it was a nasty time, bleak, but at least I was just 16. I think with such sympathy for someone like Dean Ashton, who played for West Ham: great footballer, but a terrible knee injury ruined it all and by then football was his life, his living, all over."

If you could time-travel, would you go back and change things? Be a footballer rather than Doctor Who? There is for once a long, if still enthusiastic, pause.

"Probably not, you know. It affords you – I mean no disrespect to footballers, but acting allows you perhaps a more varied path or paths in your life." He was, he admits, lucky. Around that time he was practically frogmarched into applying for the National Youth Theatre by a school drama teacher, Mr Hardingham. "Yes, Jerry Hardingham. Actually I'm still in touch. My mum speaks to him a lot. I was so lucky – to get someone who can influence your life in a significant way. He rang my mum up and said: 'Look, he's an actor – he should be an actor, and he hasn't turned up for this drama festival, but please, force him to do it.' So I was forced into 12 Angry Men and of course I loved it. And it all began."

Smith made an impact in the mid-2000s – stage versions of The History Boys and That Face, and then a TV semi-breakthrough in Party Animals before he landed the role that would take him to the prime time. And this year he has been busy proving his range (typecasting's a bugger) by playing an intriguing Christopher Isherwood in BBC2's Christopher and His Kind and somehow finding time to film the one-off drama Bert and Dickie, a kind of new Chariots of Fire about a pair of real-life sculling heroes from 1948's Austerity Olympics.

But largely he has spent the past two years in Wales – lovely Wales, but not without its rain. Is he starting to fall for it? "It's odd because – there's the set and there's home, where I'm living when there. Notice, reader, that the set I'm pointing to is a crumbled croissant and home is a mug of tea. That's pretty much the extent of my life, which is quite nomadic in a way. I'll have a walk round the bay where I live – and no, I haven't really done the hills, that's bad isn't it? – but I tend to come back to London if I have any time off.

"I've just bought this flat, and yes it's furnished now but it needs pictures on the walls. I've got this big print of Jimi Hendrix – it's as huge as that window there – and I need to get that up and get cracking with those kind of things. But out there the work really takes over. The Doctor's in pretty much all of the scenes, and even after shooting's stopped you've got to spend a good deal of time doing lines for the next day. It's not a particularly social life."

Russell T Davies once said that, given the choice, he'd always go forward, "as I know what happened before. I want to know what's to come." Which way, Matt, would you go? "Truly difficult. I think there's something more frightening about going to the future. And how can you not want to go back and see a pack of velociraptors, or hide in a tree that doesn't exist any more, or go and swim in a lake where there's a shark the size of the… moon? And I even wonder what the world was like in the 30s. I've always been into history, and then recently, probably by being the Doctor – he is, isn't he, a kind of one-man historical and scientific education? – much more into physics. I recently read The God Delusion by Richard Dawkins, which ignited my interest in a scientific, mathematical version of the world. No, I'm not religious. At all. I'm an atheist."

He must, occasionally, get an evening off. "Of course. Cinema, or some other telly – I love True Blood and Arrested Development – and even go for a beer with Karen in Cardiff. And we don't really get bothered all the time. It's funny… I went to a school, and a little girl asked me what's it like to be famous. And I had to say that I didn't really know. Fine, sometimes I get recognised, but it's not me, it's the character. And my life will probably never have this period of intense recognition on the street, whatever, when I'm not playing this particular character. Brad Pitt has airports closed off for him. That's just another world."

Has he ever thought of himself in 20 years' time? "I don't know, mate. I quite like the idea of family. That's probably the greatest achievement in the world. I've got a lot to achieve workwise – I'd love to direct – but family would be good. I'm just aware I'm in a very fortunate position just now. I remember how it feels not to work, so I'm so grateful for the chance to do so while I can.

"And yes, it's hard work, but it's all relative, isn't it? The Cardiff filming for the 50th series kicks off again in late February and I know it will be… cold. God. Minus 15 last time. Every other production – Casualty, everything filmed in Cardiff – just stopped. Doctor Who marched on. It's truly tough. But I say that. I've got a mate, Luke, who's a builder, and he says about three, four o'clock on a building site, that's when it gets bitter cold, so when I'm freezing at that time, I think: I bet Luke's colder. And he hasn't got hand warmers and a big coat and someone saying: 'Do you want a hot-water bottle?'"

Ah, hot-water bottles. So you and Daisy aren't moving in together yet? I asked this, of course, before they'd split; he seemed, back then, happy to talk about it, and happy about her. "No. No! She's got a very girly house, and there's no way in hell she'd want to move in with me. Yes Euan, you're right, particularly not with a gigantic Hendrix print – thanks for pointing that out."

A couple of weeks after Matt and I met the Sun splashed on their break-up with the thoughtful headline "Sexterminate!" Ah, hell, they're young, it had only been 18 months, I suspect they still have each other's phone numbers, much is reversible at 29 and, regardless, I doubt that pretty, sharp, enthusiastic Matt will die a loner.

As noises are being made about photos I congratulate him on having boosted the perception of Harris Tweed. "Yeah, they got in touch and thanked me. Didn't send me any bloody tweed, though. If you're listening, Harris… hmmm. I'm joking. Sort of." It was an old jacket of his own – "about 40 quid from a vintage shop about five years ago" – which he'd brought along to the audition which became the incarnation and was then coupled with a bow tie, to winning effect.

Could he now tie a bow tie himself? Mr Smith is refreshingly honest to the end. "No. It's a clip-on. But I do tie my own boots. Look, these are my boots – we have them made, these are my Doctor boots. I've never loved any footwear more." And he asks me, with grins which actually seem to bounce, to tell him more, much more, about the staining of tweed in buckets full of urine.

The Doctor Who Christmas Special is on BBC1 on Christmas Day