With hell-raising Irish screen legend Richard Harris for a great-uncle on her mother's side and a direct line to 19th-century music hall great Marie Lloyd on her father's, it's no surprise that Annabelle Wallis chose acting as a profession.

"I think it's in my genes," the 28-year-old laughs. "I grew up very far from that world, and yet here I am."

Born Annabelle Wallace in Oxford, she was raised in Portugal because, she says, her mother wanted an adventure and Lisbon seemed like a good place to have one. She attended an international school - "there were 42 different nationalities in my year," she says proudly - and is fluent in Portuguese, Spanish and French.

In November she'll be at the wedding of her cousin Jared Harris, Richard's son who is best known for playing Lane Pryce in US television hit Mad Men. But for much of her Iberian childhood, Harris himself was a distant figure.

"I'd only see him at family events," she says. "It was strange: I wasn't really aware of how big he was until I came to London and became an actor full-time. Then, going out to LA and spending time there with my cousins [Jared, James and Damien Harris, all either actors or directors], I got a real sense of the phenomenon he was and what he contributed to cinema. But I don't want to ride on those coat tails. I want to forge my own path."

That path, which has already led her to roles in The Tudors, Madonna's directorial debut WE, and American show Pan Am, takes another turn this week with the launch of bold new BBC drama Peaky Blinders. Set in the Birmingham underworld a year after the end of the First World War, it opens to menacing Nick Cave song Red Right Hand, features a rock soundtrack throughout and, thanks to a script by Steven Knight, is rough, ribald and sweary. More Boardwalk Empire than Crossroads Motel, in other words.

Cillian Murphy plays Tommy Shelby, brains behind the gang known as the Peaky Blinders for their habit of sewing razor blades into their caps. Sam Neil is his nemesis as Inspector Chester Campbell, a god-fearing Ulster Scot drafted in to bring down the Catholic Shelby clan. Helen McCrory, meanwhile, is the Shelby matriarch, Aunt Polly, and Wallis plays young Irish immigrant Grace Burgess, who finds work in the Blinders' local pub - and catches the admiring eye of Tommy. In one scene she sings The Boy I Love Is Up In The Balcony, a song made famous by Marie Lloyd.

Providing the political and social backdrop to the drama are the ongoing trauma experienced by returned veterans of the war, the start of the Irish War of Independence, and the Suffragette Movement.

"There are so many poignant historical paths at that time," says Wallis. "I think it was a very uncomfortable time politically and socially, and I feel it's quite a brave project in that sense. It makes for interesting television. Also, the Peaky Blinders are sharp dressers. They represent the youth culture of the time so there are many through-lines to the youth culture of today and to the gangs of today … It's a period drama, but it's also cool, sexy and bold."

The same could be said of The Tudors, the sprawling historical drama created by Michael Hirst for Showtime, the US cable network which also gave us Homeland and Dexter. It starred Jonathan Rhys Meyers as King Henry VIII and became a proving ground for a roll-call of young British acting talent that included Henry Cavill (most recently seen playing Superman in Zack Snyder's film Man Of Steel), Ruta Gemintas (later to star in BBC Scotland's Lip Service) and Natalie Dormer (now in HBO smash Game Of Thrones). Wallis played Jane Seymour, taking the role from Anita Briem for seasons three and four.

"It taught me so much," she says. "The Tudors was ground-breaking in the sense that it did ruffle the feathers of classical historians and alter the way people did period drama at the time. But it was the biggest-selling DVD for three years in a row, and [creator] Michael Hirst is a historian and really knows what he's doing. So I think that marriage between a pioneering network like Showtime, and good writers and actors, gives you a winning formula. The Tudors really represents that."

A less happy foray into the world of American networks came with Pan Am, set in the then-glamorous world of airline cabin crews at the start of the Jet Age and dubbed "the female Mad Men" when it premiered on ABC in 2011.

Appearing alongside Christina Ricci, Wallis played English stewardess Bridget Pierce who, as well as dispensing Bloody Marys and pretzels, worked as an MI6 courier. Despite winning the Best Series award at the European equivalent of the Emmys, the show was cancelled after a single season.

Was Wallis surprised the show was axed? "I suppose I was, because of the hype it got at the start," she admits. "When we were in talks to do it, it was sold as such a great idea - a female-driven show - which is why we were all on board. And it was something that we were all very proud of. But you can never control these things. I think it was ahead of its time in a sense."

Next up for Wallis is another meaty role which again involves period costume from the mid-20th century, as James Bond creator Ian Fleming's lover Muriel Wright in Fleming, a new four-part drama from Ecosse Films which screens on Sky Atlantic in January. Wallis plays opposite Dominic Cooper as Fleming, while Sherlock star Lara Pulver plays the author's wife, Ann Fleming.

A beautiful, dynamic, polo-playing socialite, Wright met Fleming in an Austrian ski resort in 1935 and is thought by many to be the archetype for the Bond girls who are as much a feature of the novels as the spy himself. Wright was 26 at the time, daughter of eminent Tory MP Henry FitzHerbert Wright, and worked intermittently as a model - scandalous behaviour for a woman of her class in that era.

"She was at the top tier of British society but she was quite the rebel, she would go against the grain," says Wallis. "Mat Whitecross, the director, described her as a hippy before her time."

During the war, Wright worked as a dispatch rider in London and was killed in a bombing raid in 1944. Fleming wore her bracelet on his key ring for the rest of his life and the closest literary description he gives of her is in the character of Countess Teresa di Vicenzo in On Her Majesty's Secret Service.

In the novel, Bond marries Teresa - guilt on Fleming's part, perhaps? - and, like Wright, she later dies. It's a SPECTRE bullet she gets, however. "Seen through Muriel's eyes, the war years in London were a very freeing time," says Wallis. "Women of that class weren't encouraged to pursue education or work then, so it opened up the world to them."

To date, Wallis's film work has been mostly confined to small parts in X-Men: First Class, and Snow White And The Huntsman. But in 2011 she appeared in WE, Madonna's time-shift biopic about Wallis Simpson. Ambitious in scope and (to put it kindly) often patchy in execution, the film was panned by critics and largely shunned by audiences. No matter, says Wallis.

"I feel quite protective of Madonna. People are so ready to cut you down if you take a risk and leave your comfort zone. So it was brave of her to do it and she made a beautiful film. She's a very strong woman who I look up to.

"She's a real icon of my generation and I felt very fortunate to have time with her and to observe and learn from her. I like to think that I represent myself as a strong woman, so to work with other strong women I find very inspiring."

Confident, smart, ambitious and just a little bit belligerent when she needs to be: perhaps a talent for acting isn't the only quality Annabelle Wallis shares with her great-uncle.

Peaky Blinders is on BBC Two from Thursday. Fleming airs on Sky Atlantic in January