"Fallible characters are more interesting than superheroes in the end," declares Damian Lewis. The red-headed English actor has frequently struck gold playing flawed, imperious protagonists, most recently as a lean King Henry VIII in the BBC's adaptation of Hilary Mantel's Tudor saga Wolf Hall and as soldier-turned-terrorist Nicholas Brody in Homeland. Previous subjects include Jeffrey Archer, in a biopic, and Soames in The Forsyte Saga.

Throughout his career Lewis, 44, has hardly eschewed film and theatre, yet every one of the aforementioned roles has been for TV. His latest small-screen encounter with vulnerable mastery is playing New York hedge fund titan Bobby Axelrod in the new drama Billions. Axelrod finds himself under investigation for insider trading by a US government attorney, Chuck Rhoades (Paul Giamatti).

Appropriately, since Lewis has been at the vanguard of the recent golden age of television drama, his antihero in Billions is the quintessential cable TV drama Bad Person Who Does Good Things. A rapacious dealmaker suspected of financial illegalities, Axelrod is also a 9/11 survivor who pays for the college tuition of colleagues' families who died in the World Trade Center attacks and who steps in to save his neighbourhood pizzeria from closing.

When we meet in New York I ask Lewis what accounts for his fascination with fallible characters. "They're very human," he replies. "If you have the same drive and passions that everybody else has – for example if you're trying to do the right thing for your family and do the right thing for people you employ – then you can be forgiven quite a lot.

"Some of the characters that I've played recently have a sense of destiny and a sense of moral purpose and I like that about them. Sure, they're compromised and sometimes they do despicable things, but for some reason they're never not likeable."

Billions, like Homeland, is produced by the US TV cable network Showtime (it will air on Sky Atlantic in May). The network is clearly hoping that the show will ignite debates about the super-rich and income inequality comparable to the conversations that Homeland provoked about the war on terror. The relationship between Axelrod and law enforcement official Rhoades is reminiscent of US Attorney for the Southern District of New York Preet Bharara's investigation into hedge-fund billionaire Steve Cohen (further blurring the lines between fact and fiction, Bharara turned up to the premiere of Billions at Manhattan's Museum of Modern Art). "We're looking at a tenth of the 1 per cent and at what's fair and what's not fair," says Billions co-creator Brian Koppelman.

In the wake of Wolf Hall and Homeland, Lewis's market value is higher than ever. A recent New Yorker profile of Lewis revealed that Patrick Wilson was the first choice to play Brody in Homeland. Yet Lewis's presence in the show opposite Claire Danes proved such a draw that plans for the character to be killed off during the second series were abandoned and he survived until the end of the third series. This time around Showtime won't be shorting its star any time soon. "What better man than Damian to play that big-baller New York hedge fund-type guy?" says Matt Blank, CEO of Showtime.

To research the role, Lewis spent time with prominent hedge-fund moguls Daniel Loeb, Bill Ackman and Larry Robbins. His entry to the world of elite financiers' yachts and private jets was supplied by Andrew Ross Sorkin, co-creator of Billions and an influential New York Times columnist whose best-selling book Too Big to Fail, chronicling the 2008 financial crisis, was made into an HBO film which also featured Giamatti, playing Federal Reserve chairman Ben Bernanke. Sorkin was in awe of Lewis's research techniques: "Not only did he read books but he would send me emails in the middle of the night asking about the moral code of the character. We would go round different hedge funds and he was really into it."

Lewis was educated at Eton and it's more than likely that a few of his classmates wound up in the City. What does he see as the difference between billionaires on the Square Mile and Wall Street? "Hedge funds in New York are bigger – something happened on Wall Street with the sub-prime mortgage crisis that had repercussions throughout the world. This isn't a show about that world but nevertheless it stems from it."

Class reared its head recently when former students at north London comprehensive school Acland Burghley took umbrage at Lewis opening the 50th-anniversary celebrations of the school given his own privileged education. Class is also a theme in Billions. "My character is from Yonkers, just north of the Bronx so he's a blue collar guy made good," says Lewis. "He's a very American animal and New York animal in his pugnaciousness, his focus and the way he speaks. He's not a generic hedge-fund guy."

Damian Lewis's market value is at an all-time high (Showtime)

Lewis's last stage appearance was playing the desperate hustler Teach in a West End revival of David Mamet's American Buffalo alongside John Goodman and Tom Sturridge. He's quite clearly drawn to playing characters at the extremes of life. "Sometimes," he responds. "But it's the quality of the writing and the theme of the piece that is key." Lewis's dedication to the material is borne out by a story I heard; it seems that he agreed to do American Buffalo after bumping into producer Matthew Byam Shaw in the loo of the Savoy Hotel at the Evening Standard Theatre Awards. Until that point he had been in negotiations to appear opposite Tom Hanks in Ron Howard's latest Dan Brown adaptation, Inferno, but instead opted to be in American Buffalo, one presumes at a financial cost, though probably not at a cost to his career reputation.

Billions revolves around finance, so contains lines such as "You see that block trade last Thursday come out of Merrill?" Films and TV series about money more often than not don't end up making that much of it. Showtime supremo Blank acknowledges this: "The real question is: can you take this type of subject matter and make it broadly appealing? It's a New York show but we don't want it to just be for New York viewers."

When I interviewed the film director Brian De Palma half a decade ago, he lamented casting Tom Hanks and Bruce Willis in The Bonfire of the Vanities, his notorious 1990 flop film adaptation of Tom Wolfe's best-selling novel chronicling 1980s Wall Street excess. "It was miscast – I should have made it like The Sweet Smell of Success," De Palma reflected. "If I was making it today, I would probably cast one of the English actors. You need an arrogant blue-blooded rascal, someone who everybody hates but who has style."

This has come to pass with the casting of Lewis in Billions but Neil Burger who directed the pilot episode admits nationality was still an issue. "It gave me pause," he said. "Do you want an American playing an English earl? Maybe not. But in this case the Brit playing the guy from Yonkers has such power and swagger, and the show is really about power."

Sorkin concurs: "Damian can do power better than anyone else. He can do it in a hard way and, more uniquely, he has a soft power." What do Sorkin's billionaire hedge-fund acquaintances think of the show, assuming they have found the time to watch it? "Those I've spoken to think it's fun," he says. "All of those guys think it is really about themselves."