With bloodshot eyes, a crumpled suit and the rueful air of a man who has had one too many Martinis, Jon Hamm, just for today at least, is feeling a little Don Draper. Last night was a late one. Dinner at The Wolseley followed by drinks back at his hotel bar have left him a bit broken. It is 11am and this is his fourth interview of the day, starting at some ungodly hour with a baptism of bosomy fire courtesy of Lorraine Kelly and followed by a stream of ebullient radio presenters. He cradles a black tea, wincing every time crockery crashes in the kitchen of the backstreet London cafe we're seated in. But Jon Hamm isn't one for a whinge. While smiling may not be a characteristic of Draper, the role he has played in the extraordinarily successful US TV series Mad Men for four years, Hamm, hangovers aside, is very much a different man.

He is funny. Perhaps surprisingly for a person who plays dour so well (as well as Mad Men, recent film outings The Town and Howl have played on his serious side), the comedy has always been there. It's how Hamm, 40, met his current co-star, Kristen Wiig, Saturday Night Live staple and writer and star of Bridesmaids, the film that brings him to London today. He has hosted SNL three times alongside Wiig, co-creating their skits each time. Then there was 30 Rock, where he played Liz Lemon's love interest, Dr Drew Baird, for six episodes. But it is Bridesmaids, which he signed up to without so much as even reading the script, that will really prove Hamm's talent at flexing his funny bone.

"You're talking about my penis, right?" he quips as quickly as the words "funny bone" exit my mouth. "It's nice. Playing a character like Don Draper tends to colour people's interpretations of you …"

His character in Bridesmaids, however, is not entirely dissimilar to that of rakish Draper. As Ted, he is the handsome breaker of hearts, in more of a laughable fashion than Draper's inbuilt 60s misogyny, but with that same disregard for monogamy that the Mad Men lead so excels in.

"I seem to be the go-to douchebag," Hamm grins. "I don't know if that's something I'm particularly proud of. I guess it's a bizarre thing to be able to play a terrible person convincingly, but I was honestly just so happy to be asked to be part of the film that I said, 'I'll play whatever you want.' I'm a very great fan of Kristen's; every movie she's in she's made better, even a two-minute scene in Knocked Up. She's a force, and she very much deserves her moment."

In the US, Bridesmaids has been a runaway success, taking $90m dollars in the first three weeks, a hit that nobody in the industry foresaw. It had been dubbed "the female answer to The Hangover" – a niche women's film – but to pigeonhole it in such a way is to do it a huge disservice. While the story focuses on a group of girlfriends in the run-up to one of their weddings, the humour is universal.

"There are some things that are undeniable in their comedy appeal," Hamm agrees. "Whether it's Bugs Bunny or Monty Python, you fill in the blank. You can't watch Fawlty Towers and not laugh. While there are things [in Bridesmaids] that will be funnier for ladies, or for guys, there is a larger pot which is just funny."

'I was only on set for two days, but they were two of the most fun days I've ever had in my entire life'

Bridesmaids.

A particular scene that will no doubt cross the sex divide is that of Maya Rudolph, as a bride-to-be in full wedding regalia, suffering an acute case of food poisoning in the middle of the road. "That is a funny, funny scene," Hamm laughs. "Full credit to [director] Paul Feig and [producer] Judd Apatow for fighting to keep that in, but also to Maya, sinking to the middle of the street in her wedding dress." Hamm himself serves as the butt of many jokes in the film: a comical stereotype, the cartoonish alpha male. As Wiig's character's part-time lover, he is a delight to the eye and an assault on the brain.

"I'm not sure being the joke is something that I enjoy," he laughs, "but it serves a purpose and somebody's got to be that guy, so why not me? I was only on set for two days, but they were two of the most fun days I've ever had in my entire life."

Hamm plays a brilliant rogue, there's no denying the fact, but his own life is a far less lurid affair. He lives in LA, out of sight of Hollywood's neon glare, with his partner of 14 years, actor and film-maker Jennifer Westfeldt. Public appearances are limited to promotional activity, his favourite restaurants are quiet corners away from the paparazzi. "Fame is such an ephemeral concept," he sighs. "When you attach it to a Kardashian and a politician with equal weight, it's just silly. It's useful, it helps you get movies made, but, boy, is it a double-edged sword. I try not to be bothered about it, simply because it's so strange, but it's no fun to have people take pictures of you picking your nose on the street or picking up your dog's poop."

To have such a measured view of the trappings of fame can only have been encouraged by the late start with which he came to it. He was 36 when Mad Men first aired, and until that point merely another struggling actor. Born in St Louis, Missouri, Hamm was raised by a single mother until the age of 10, when she died of cancer. He moved in with his father, with whom he stayed until he too passed away, when Hamm was 20. To say that the influence his mother had on his formative years still runs deep would be an understatement. From his views on marriage (he has often spoken of the fact he doesn't "have the marriage chip") to his thoughts on feminism, she is ever-present.

"My parents were divorced in the 70s," he says. "I think I was the only kid in my grade school who didn't have married parents. My mom was relatively young and raising a kid by herself, so I do consider myself a feminist; I get that sensibility. I'm certainly not a misogynist, no way, man; I'm down with the strong ladies. With Jen, there is no alpha, we both rule the roost. I don't think anybody should be king of the castle, it's a little bit more of a teamwork situation."

The teamwork is something they have brought to film in the past, with Kissing Jessica Stein, the 2001 film Westfeldt wrote and they both featured in. Next up is Friends With Kids, written and directed by Westfeldt and starring the couple, alongside Bridesmaids alumni Kristen Wiig, Maya Rudolph and Chris O'Dowd.

'I think it's good for things to end, and Mad Men is no exception. There will need to be a last chapter'

"It's a new experience for me," he says of his role as producer. "Jen has produced all three of the films she has made, but for me it's brand new. Fun and scary. There is a moment where you think, 'This is all going to fall apart, this is not going to happen,' and then it does happen. Like most things in life that are worth a shit, it is thrilling and terrifying all at once."

He is also to have his first experience of directing, thanks to Mad Men. Hamm will direct the season five premiere of the show. "The decision came out of figuring that if I was ever going to get an opportunity to do something like that, this is the perfect place," he explains. "I'm surrounded by people I know, everybody wants it to succeed, so there's a team-oriented effort."

Mad Men seemingly still brings Hamm as much joy as the first time he played the role of Draper, following a notoriously strident seven-audition process. "We get the scripts and we read them like these weird little fans," he laughs. "'Oh my God, did you read that bit?' It's really fun, I'm an incredibly lucky guy and I get to work with people whose work I respect tremendously, who are at the top of their game. But I think it's good for things to end, and I think our show is no exception. There will need to be a last chapter."

That last chapter, according to Hamm, will not come for at least three seasons. While he will be sad to say goodbye to the character who undeniably made his career, there is no doubt that the work will keep on coming. "I wish I had a better way to describe it than this," he says, "but I've just been incredibly lucky." Whether it is luck or years of persistence, Hamm finally has Hollywood where he wants it. And although he may forever be associated with Mad Men, as Bridesmaids should help prove, there is more to Jon Hamm than Don Draper.