There was a time when Harry Lloyd worried that he was forever going to be typecast – as a woman. As a reedy-voiced first year at Eton, he played the lady in one-too-many all-male Shakespeares. "After that I swore: 'I will never play a woman again.' You're at a boys' school and you're 13 and, yes, I love acting, but I don't have the balls to do that. Normally on stage you feel cool and confident, but I was wearing a bonnet and a fake bra and I felt miserable." Then, in the sixth form, his English teacher begged him to play Rosalind in As You Like It. He hesitated but, a true pro even then, stepped up for one final fling.

"I thought: 'You know what? Screw those boys in their suits chuckling in the back row. I'm going to stand up, put on the make up and do it.'"

That pigeonhole dealt-with, another loomed for the precocious teen – this time on television. Aged 15, he landed his first professional role in the BBC's David Copperfield, opposite fellow unknown, Daniel Radcliffe, followed, a few years later, by a role in Goodbye Mr Chips. A life in breeches and top hats seemed to beckon for the public schoolboy who, in a headline-friendly twist, happened to be the great, great, great grandson of Charles Dickens (of which more anon). "I got scared after that, that I'd spend my life in period dramas or would forever be playing Etonians. But that made me think: 'Right, diversify.'"

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And diversify he did. Over the past five years Lloyd has played everything from a schoolboy possessed by aliens in Dr Who to one of Robin Hood's merry men. On stage, he's run the gamut from Ibsen to LaBute, with roles as a rent boy (opposite Gemma Arterton in The Little Dog Laughed) and an Italian New Yorker in a knockout A View From The Bridge in between. Today, the actor – slight and rangy in a kitchen porter ensemble of black-and-white checks and scruffy skater shoes, with a whiff of the estuary about his accent – looks and sounds much like any 27-year-old Londoner. Stick him on stage or in front of a camera, though, and he transforms. With an androgynous, high-cheekboned charm that appeals to boys and girls, there's both a fragile, thin-lipped intensity to his performances and an intelligent, twinkly wit, making him at once utterly memorable and utterly impossible to pin down.

His next three roles are suitably diverse: playing Rochester's brother-in-law in the starry new Jane Eyre movie, opposite Mia Wasikowska and Judi Dench, the young Denis Thatcher (to Jim Broadbent's older version) in much-hyped Maggie biopic, The Iron Lady – starring Meryl Streep – and a beggar king in HBO's epic new series, Game of Thrones, which starts next week on Sky Atlantic. Billed as The Wire crossed with Lord of the Rings and based on George RR Martin's bestselling books, it's the channel's first foray into fantasy. And it hasn't taken any chances. The budget is rumoured to be between $60-$100m ("Big enough that they can spend $10m on a pilot and scrap most of it," confides Lloyd), most of which which has been splashed on CGI, fake snow and a star-studded cast, led by Sean Bean: think Rome with dragon eggs, dwarfs and twice as many spilled entrails. Lloyd plays Viserys Targaryen, an exiled noble fighting for the Iron Throne of Westeros. Among myriad distractions, his Machiavellian, incestuous brat in a silver wig sneakily steals the show.

"I wasn't a fan before, but when you get into the books, it just releases your inner geek," says Lloyd. "It can be very staid and dry when people are talking about kingdoms. You have to engage with it; have some fun." He spent half of last year filming between Belfast and Malta. It was his first brush with big-budget American production values and he loved it. "I liked working for people with lots of money. You can't do it with 20 extras. If you're not going to make it complicated, wiggly and morally ambiguous, with a cast of 160 or so, what's the point?

"If you're just going to reduce it to Ned Stark against a guy with white hair – well, we've already been to Mordor and done all that," he says. "Adult fantasy gets a bad name. You think of Xena – Warrior Princess. If you don't do it expensively, it becomes tacky and you end up just appealing to 45-year-old single men."

Lloyd, a "friend of Comic-Con" [the world's largest sci-fi/ fantasy fan convention], thanks to roles in Robin Hood and Dr Who, knows what he's talking about. His appearance in the latter as a bully whose body is taken over by the villainous Son of Mine impressed Russell T Davies so much that he sent a note to the casting director, saying: "That's the next Doctor. Seriously. He's so brilliant." Lloyd was filming the second series of Robin Hood in Budapest when his agent called to tell him that he was being touted, feverishly, as David Tennant's successor. He wasn't, of course. "No one has ever spoken to me about it. But that's alright." Would he want the part? "I'd have to think very carefully," he says. "It's not a decision to be made lightly, as the schedule is nine months of the year and it's exhausting."

As ever, Lloyd would rather keep his options open – especially now that HBO has flung open the doors to Hollywood. As soon as he was cast as Viserys, the American agents came "sniffing around". Deliciously, he was on stage in the movie industry satire The Little Dog Laughed at the time.

"They'd come to London and see me in this play about morally reprehensible American agents. And afterwards, these lovely, glammed-up, middle-aged women would come into my dressing room and say: 'Hi, that was great – loved that play. Loved it.' And I'd think: 'Really?'"

He eventually signed to one and flew out to LA a couple of times last year. "It's a funny place," he says. "They love getting you in the room, introducing you: 'This is our new guy: he's the best thing since cheese...' But it was also very nice to not be available – I had to come back and film Game of Thrones. So rather than joining the queue, it allowed me to sit back and audition them a little bit." If that sounds over-confident, it's just Lloyd's way. "I've always thought I'll do this for the rest of my life. You've got to be confident. You can't think: 'Well, I'll just keep my carpentry course up my sleeve.' No. You romantically believe that, whatever happens, I'll do it for a living. Maybe I haven't been tested. Maybe talk to me when I've been out of work for four years and we'll see."

Certainly, Lloyd has barely paused for breath so far. Born into an arty family in Hammersmith – his father is a literary agent and his mother is in publishing, while his sister is a radio producer for Heart FM and his little brother does photography – he was a "bookish child" who fell for drama early on. He tells me a long, involved story about how he won his first lead, in The Adventures of Sir Gervase Beckett, by knowing which word to emphasise in the opening line at his audition. He was just eight years old.

This cerebral, conscientious approach to acting has stayed with him ever since. Before The Little Dog Laughed, he set up a meeting with a New York rent boy to "demystify" his part and spent months getting to know Viserys – "You almost rewrite the books," – for Game of Thrones. When he didn't feel that he understood his part in The Sea (opposite Eileen Atkins at the Theatre Royal Haymarket), he tensed up and promptly lost his voice.

Following in the footsteps of Eddie Redmayne and Tom Hiddleston, Lloyd began his career at Eton. He "squeezed the opportunities dry" there and was soon spotted by a BBC scout during a play rehearsal. By the time he left, he already had an agent (via a failed Harry Potter audition) and was well on his way. "I was waiting for someone to tell me: 'OK, enough of that, now get yourself a real job.' But no one ever told me to stop. So I didn't."

He chose to study English at Oxford over drama school, thinking: "If I don't use this bit of my brain, it'll shrivel up and die." He still spent most of his time at Christ Church acting in plays, including a Much Ado About Nothing opposite fellow rising star Felicity Jones, living in Cowley ("The posh boy trying to get real...") and writing his thesis – on Dickens, naturally.

The family link is on his mother's side. "It's great. If you're going to be related to someone it might as well be Dickens," he grins. "Really the best thing about it is that I know a lot more of my cousins than I might otherwise. But I'm very proud of it and I do quite enjoy how people congratulate you for it, even though you've done nothing to deserve it. It's like I was born with an extra finger – it's just one of the things that I came with."

These days, he lives in east London, the grimy heart of Dickens' city. "Sometimes you're wandering late at night and you can see it and feel it and hear it. This was a man who would spend two, three hours a day walking the streets of London, listening to people he had no business to be in touch with, just picking it up. Not a lot has changed – all the different jargon and patois, and ways of clothing and jewellery. I think he'd have loved it."

He wasn't always so at home with his literary heritage, paranoid as a teenager that he'd only won his first part thanks to a ghostly family tie.

"I was in massive denial. I didn't want to be stuck in Dickens period dramas because then I would never know if I was any good. It's only now that I've got out of my breeches and played rent boys and Italian immigrants and kings of wherever that I can think: 'Oh, OK, I'm doing alright at it. It's not all nepotism.' Now I can enjoy it."

'Game of Thrones' starts on Monday at 9pm on Sky Atlantic