It’s another sunny day in LA. Seeing as I was coming to meet the man who has done more to raise male sartorial standards than just about any other living person – did anyone wear a pocket square pre-Mad Men? – I’ve decided to sport a nice linen jacket and tassel loafers. But Mr Jon Hamm is dressed down in an NHL cap, a red, white and blue checked shirt, dark jeans and Converse, plus a couple of days of stubble. “Jesus, you look so smart,” he says. “I look like a suburban dad who’s got lost on the way to school.”

He recently worked out he’d spent longer in LA than anywhere else and, well, there have been ups and downs. But of the ups, the eight years he spent on Mad Men, Mr Matthew Weiner’s drama set in a 1960s New York ad agency (2007-2015) threaten to reduce everything else to a footnote. As he is all too aware.

This is the man who played Don Draper, the most iconic male in perhaps the most iconic show in the Golden Age of TV. He’s the man who recalibrated masculinity, who repopularised the old fashioned, whom women wanted to bed and men wanted to be, even though everyone knew what he was selling was a lie, that he was, in Mr Hamm’s words, “a fundamentally fucked-up human being”. He’s among the most objectified males on the planet. “It is not easy having immediate and huge-scale fame thrust upon you. I’m a pretty shy person. I like talking to people one-on-one, but I do not like people taking pictures of me with 400mm lenses across the street. It’s mystifying to me why we give that any time in our culture.”

Soon after the series ended, Mr Hamm split with his partner of 18 years, the film actor/director Ms Jennifer Westfeldt, and checked into rehab for alcoholism. Around that time, The New York Times asked: “Is there life after Don Draper?”

Let’s hope so. Mr Hamm is not only one of the most likeable stars in Hollywood – he says he owes his career breaks mainly to being “nice”, respectful of people’s time, listening, preparing – he’s also a damn fine actor, belatedly honoured with an Emmy for that final season.

There’s a certain Midwestern modesty to him. He makes clear that his relationship is not up for discussion (“It’s very personal and specific and I think people tend to draw their own conclusions about that anyway”), but the implication is that he’s single. However, he’s upfront about almost everything else right up to the moment he has to leave for his weekly therapy session. “I find it very helpful,” he says. “I know the English are a lot more sceptical about it than Americans are, but maybe after Brexit, you’ll change your minds.”

As for rehab? “It has all these connotations, but it’s just an extended period of talking about yourself. People go for all sorts of reasons, not all of which are chemically related. But there’s something to be said for pulling yourself out of the grind for a period of time and concentrating on recalibrating the system. And it works. It’s great.”

Even in his baseball cap, at 45, Mr Hamm is as comely as you’d expect from a man whose first credit was “Gorgeous Guy at Bar” in an episode of Ally McBeal. One women’s magazine described him as “astronaut handsome”, not that astronauts are selected on looks, duh, but it does capture his capable, reassuring, 1950s air and captain-like quality. His voice really does insinuate that everything’s going to be OK, but there’s something soulful about him, something indefinable that makes you hope he’s going to be OK, too.

This year, he’s spending Christmas at his aunt’s on the Californian coast, most likely, but can’t think of a thing he wants for Christmas. “Having come from a fractured family, holidays were always a little catch-as-catch-can.” He lives in Los Feliz, as he has done since he moved to LA, and can often be seen at his local Italian deli, Little Dom’s. Is settling down, having kids on the agenda at all? “I don’t know. I don’t think it’s necessarily an imperative. I’m not going to psychoanalyse myself here, but… well, never say never. I’ve got nieces and nephews and I’ve been a teacher. I’ve probably been around kids a lot more than all my friends. I feel if you shut that off entirely you calcify. You turn into that guy.”

He means the guy who complains about what the kids are up to these days, though he does express a certain bafflement at social media. “I speak to young kids starting out and they can’t even get into an audition unless they have a certain number of followers on Instagram. Of course, it doesn’t mean anything – you can go out and buy 100,000 followers. But it becomes meaningful if business decides it’s meaningful. In time there will be a correction and we will look back on this period and say, ‘Wow. We were really dumb.’”

There’s a careworn legend that Mad Men creator Mr Weiner remarked after his first audition, “Now there’s a man who wasn’t raised by his parents,” which is partly true. Mr Hamm’s parents divorced when he was two and his mother, Deborah, died of stomach cancer when he was 10. He moved in with his father, Daniel, a flamboyant character who had sold a trucking business and pursued various jobs, but mostly he was brought up by friends’ mothers. “I was always fascinated by my dad because he could talk to anyone. He was a great listener and he knew a little bit about a lot of things. I aspired to be like that.”

Happily, he was sent to a school – the private John Burroughs – that pushed a broad curriculum (his mother had put aside her secretary’s wages to pay the fees). “You were rewarded for taking an interest in a lot of things. In the first couple of years, you were required to take every single elective: speech, debate, math, arts, gym.” He was good enough at baseball and American football to take them further, but it was drama that he found most rewarding. “I just wasn’t that interested in lifting weights all day to become an athlete – I sensed the diminishing returns. I still play baseball, but I like it more as an avocation rather than a vocation. Drama was one of the only things I kept coming back to and kept being rewarded for.”

Such is his admiration for his school, Mr Hamm returned to teach for a couple of years after finishing at the University of Missouri. By then, his father had died, leaving him an orphan by the age of 20. It was one of his half-sisters who finally convinced him to seek professional help and he’s been an advocate of therapy ever since. “After I’d lost my dad, I had this horrible paralysing inertia – and no one in my family was capable of dealing with it. So what do you do? Go and see a professional. I preach it from the mountaintops. I know it’s a luxury and it’s not something everyone can afford. But if you can, do it. It’s like a mental gym.”

At 24, he moved to Los Angeles to give acting a shot. “I decided to give myself until I was 30.” What happened next has become one of the most repeated origins stories in Hollywood – often compared with his Mad Men trajectory from gawky Dick Whitman to suave Don Draper. He spent years in the wilderness of low-rent dramas, waiting tables, even a spell as a set dresser on a porn film, which he describes as one of the most depressing experiences of his life.

As he turned 30, he got his first movie: We Were Soldiers with Mr Mel Gibson. “I had a small part in it, but I made a ton of money on it. I thought, OK, I’m working now. I don’t have to do a shitty day job anymore.”

He is reliably damning about the character who eventually made him famous and I think he needn’t be. WWDDD (what would Don Draper do?) is a fairly reliable vector of how to behave in a pressurised situation – if you dispense with all the self-loathing and womanising. “I guess what was so attractive about him was this cool confidence. That was his decision. He came from an unstable, strange place, and figured out that he had to project this aura of command and that people would follow it.”

It’s not something that he’s taken on – “I’m not interested in fucking with people” – but he does credit Draper with improving his wardrobe. “I don’t share a lot of sartorial clues with Mr Draper, other than we’re the same suit size, but it did open my eyes to buying clothes that fit properly. I generally try and dress a little more appropriate to my age. It’s epidemic out here. So often I’m like, ‘What are you wearing? You have an Ed Hardy T-shirt and a wallet chain and biker boots and you’re 65 years old?’”

His latest role is in a Mr Greg Mottola spy caper called Keeping Up With The Joneses. Mr Zach Galifianakis plays the sort of mediocre suburban dad you can imagine Mr Rick Moranis or Mr Steve Martin taking on in a more innocent movie era; Ms Isla Fisher is his cute but undersexed wife. Then one day, the suspiciously perfect Joneses move in (Mr Hamm and current Wonder Woman Ms Gal Gadot) – only it turns out they’re spies, and after much counterespionage and hijinks, bromance blossoms between the two men. It’s not the most challenging fare, but as Mr Hamm says, “It has a good heart. There’s something about that I find appealing. I feel like comedies these days are so mean. If the punchline of the joke is ‘Fuck you!’ you’re bullying the laugh out. I feel like you can take your aunt to this.” He and Mr Galifianakis are old buddies from back in the 1990s, when they both used to hang around the Largo comedy club with comedian Ms Sarah Silverman.

As rewarding as the Don Draper role was, he is mindful of the need to keep a distance. His most high-profile big-screen roles have been as a cop in the Mr Ben Affleck crime thriller The Town and as a sports agent in the Disney movie The Million Dollar Arm, with quirkier comic turns in Black Mirror, 30Rock, Saturday Night Live, Unbreakable Kimmy Schmidt and A Young Doctor’s Notebook, opposite Mr Daniel Radcliffe (“I called him and said, ‘Hey, if there’s anyone who knows how it feels to be defined as one thing, it’s me’”).

“Once Mad Men blew up, it was a conscious decision on my part to pivot away from all that,” he says. “It’s no secret that I was offered a ton of parts that involved a hat and a cigarette and a glass of brown liquor. But I was like, I do that already. I played Don Draper for 93 episodes – that’s enough. If you just want to do the same thing again and again, why get into acting?”

He has turned down superhero movies, despite being a Marvel fan as a boy. “I was very hesitant to be involved with any of that stuff. It takes so long as they don’t want one movie, they want three movies with two crossovers… You’re [just] doing it for the exposure.”

Still, I sense a frustration when it comes to more serious films. “From a features standpoint, it’s really difficult to get hard dramas made if you’re not Matt Damon, Christian Bale, Denzel Washington or Ben Affleck. That’s what those boys do and there are only so many slots. There are five or six leads who get the first look and if you’re lucky you might get a second. But hope springs eternal around this time of year. We’re done with the capes and tights and laser beams and we’re starting to see the serious movies that are up for awards.”

As we close the conversation, we move on to his hometown of St Louis, and he speaks intelligently on the recent unrest of the Black Lives Matter movement, and the anxiety creeping through the US. “Police violence is such a difficult thing to comprehend. If you sat me next to a black person who had also grown up in St Louis, simply by the nature of the colour of our skin, we’re going to have completely different experiences. It’s so difficult for people to grasp as it just rams up against our ideas of fairness and authority. The more and more shit that comes out like this, it’s harder and harder for people to dismiss.”

He feels this is a time of great disruption, but that some good will come from it. “I’m an optimist. And I do think the more we find out, the more the centre of gravity in the culture will shift. I hate this idea that nothing matters. It can’t all be a dumbshow.” He stops himself. “Sorry, that got real dark real quick,” he apologises. Something Don Draper would never dream of doing.