Nine years ago, Jon Hamm was a remarkably handsome but relatively little-known actor when he was cast from more than 80 candidates as Mad Men’s suave Don Draper. After the show’s first season, he had already won a Golden Globe as best actor, and his sharp-suited, womanising protagonist had quickly become television’s most intriguing antihero.

Now, almost a decade on, Hamm has officially achieved pin-up status, regularly polled as ‘Sexiest Man Alive’ by various publications, while the 1960s-set show has become one of the most critically-acclaimed dramas of all time. However, Mad Men’s army of ardent fans (and there are many in India, too) must steel themselves to say farewell; the show’s final seven episodes have gone on air.

“The opportunity to play a character who has this many layers and is this juicy and rich and lovely and weird and sad and horrible is like winning the fucking lottery,” enthuses Hamm, 44, when we meet on the morning of the show’s final red-carpet premiere. “It doesn’t happen often. I am continually blown away and grateful that this thing chose me.”

Has immersing himself in a character so “weird and sad and horrible” — with inescapable darkness and a deeply damaged past — come at a price, however? The night before we meet, the news breaks that Hamm spent a month in rehab for alcoholism, which, given his alter ego’s many afternoons soaked in a scotch-infused haze, seems a horribly cruel case of life imitating art.

The topic, I have been warned, is strictly off-limits but Hamm, impressively ebullient for one whose struggle with drinking is, as we speak, trending on Twitter, alludes to the demands that playing Don has brought. “It is a difficult headspace to be in for a long time,” he admits. “Acting is not a physically demanding job, like playing professional football, or breaking big rocks into little rocks, but it does take a lot of focus and mental acuity, and it takes an emotional toll. Especially when you’re playing a person with a lot of emotions; you can have a lot of sad days at work.”

The saddest of all came when the cast and crew filmed the show’s final scenes “There was a grieving process,” muses Hamm in his mellifluous growl. “Whatever the stages of loss are: anger and bargaining, but you eventually come to acceptance. We all went through a version of that to various degrees.”

I ask how hard it is to unshackle oneself from a character — particularly one as career-defining as Draper — after nine years. “You don’t need to burn sage and take a circle shower and cleanse yourself in the water of Lake Minatonka,” deadpans Hamm. “For me, it was taking off the suit, wiping the crap out of my hair, wiping off my make-up and feeling like a normal person again. The power of the costumes is so incredibly transformative. Reconfiguring yourself goes a long way.”

Today, he is still in a suit — dark grey, well-cut — but unlike his clean-shaven character, he is sporting a full beard. The fact that it is flecked with grey does nothing whatsoever to diminish his hotness, and when he pokes fun at me by briefly adopting an English accent, I am unable to contain an embarrassingly girlish giggle.

The actor’s attractiveness is a significant factor in his portrayal of Draper, according to his colleague Vincent Kartheiser, who has played the loathsome fellow ad man Pete Campbell for the past nine years. “I think people wanting to punch [Pete] in the face has less to do with his actions, and more to do with his face,” he says. “You look at Don Draper — he does just as many crazily awful things, if not more, but you don’t want to hit him. Pretty people have it easier,” he reasons.

“Yes, I think there is unfortunate wiggle room in how people are treated in the world, but that’s the way it goes,” demurs Hamm, skilfully diverting us away from further discussion of his physical charms. “But, Don has been punched in the face more than once. People aren’t shy about displaying their displeasure with Don.”

Could the wayward Draper survive in today’s more tightly controlled corporate world? “God, no,” says Hamm. “You can barely keep your own private information private now — there’s some Russian hacker who knows your waistline and credit card number. People know the backs of your retinas at this point.” He pauses. “I just watched CitizenFour [the documentary about Edward Snowden], so I’m a bit freaked out,” he explains.

“It’s terrifying how connected we all are; people need to be alone sometimes,” he continues. “Solitude can be a healing and rejuvenating thing, and it’s increasingly hard to do as we’re surrounded by screens and connection. It can be overload.”

And, while Draper has rarely made it through a season (sometimes even an episode) without committing adultery, Hamm himself has been in an apparently rock-solid relationship for 18 years, with the 45-year-old actress and screenwriter Jennifer Westfeldt, in whose film, Friends with Kids, he appeared in 2013. The couple have no kids, and as to why they have never married, Hamm is politely evasive. “I’m not against it; marriage works for a lot of people — they call it an institution for a reason,” he says. “I think everyone should be able to get married — or not. Gay, straight, knock yourself out; if that’s your jam, do it.”

I tell him that, among my friends and fellow devotees of the show, I stand largely alone in still having sympathy for the errant ad man. “I think, perhaps, there is something fundamentally in Don Draper that people can identify with — a dissatisfaction, a striving for something, a kind of ennui,” agrees Hamm. “I can certainly relate to being in a place in your life when you think, is this all there is?”

Hamm was born and brought up in St Louis, Missouri, where his father ran a trucking company and his mother was a secretary. His parents divorced when he was two, and he lived with mother until she died of colon cancer when Hamm was just ten. He then moved in with his father, who died when Hamm was 20. He has spoken in the past of “a profound sense of being alone”.

He moved to LA, aged 24, and waited tables while trying to break into acting. He struggled to win roles — which he puts down to “always looking 10 years older than I was”, and after three years, he was even dropped by his agents at William Morris. He set himself a deadline; if he wasn’t succeeding by the age of 30, he’d throw in the towel. “As soon as I said that, it was like I started working right away,” he shrugs.

The hustle, one would think, was well behind him now; as well as his Golden Globe, he’s received nine Emmy nominations, and major film roles in The Town and Bridesmaids. Nonetheless, he still talks of “staring at a phone that’s not ringing and wondering if you’re going to work again”. He adds: “I’m gainfully unemployed. I have nothing to do.”

He has consulted his friend Bryan Cranston — perhaps better known as Breaking Bad’s Walter White — on life after a smash hit. “I saw his play in Boston and we went out for spaghetti afterwards — the finale of his show was airing the next night, and he was experiencing some version of what was happening to me now,” he recalls. He also spoke to Tina Fey, with whom he appeared in the comedy 30 Rock. “None of us have been through it before, and so few people know [how it feels]. It’s hard and weird.”

Hamm has, at least, had years to process how Don Draper’s story would end; its creator, the show’s creator, the otherwise notoriously tight-lipped Matthew Weiner, outlined his plans to his leading man three years ago. The rest of the cast, however, were not party to the plot; such was Weiner’s concern for secrecy that a fake script was issued at the show’s final table-read.

But, given his track record — a fake identity, two failed marriages and multiple ill-advised affairs — a happy ending for Draper is probably something of a foolish fantasy. “My goal for Don is that he find peace,” says Hamm. “That’s a legitimate hope for a person who has not had much in his life. He has attempted to build a house, several houses in fact, on a very broken foundation and needs to address the foundation before he starts building a new house.”