Pattinson used the positive reviews to help fuel his rise to Twilight fame. Riley, who went on to star on Broadway, and in television and films, has no hard feelings.

“I would have done exactly the same thing,” says Riley, laughing, and adds with his tongue firmly in his cheek: “And as a result of that, his career crashed and burned. So what can I say?”

Riley’s career is humming along nicely and he takes another step into the spotlight this month in The Nevers, a gender-bending sci-fi fantasy series on HBO created by Joss Whedon.

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Set in England in the 1890s, the show centres on a group of people who have mysteriously been imbued with distinct superpowers. Some can see the future, some grow 10-foot-tall (three metres), others can harness electricity.

“It does defy definition and description in so many ways,” says Riley from his home in Los Angeles in the United States. “It just felt like something fresh and new. It made me realise just how long I’ve been without something like that.”

In the series, Riley plays Augie, a rather stiff member of the aristocracy who also happens to have been “touched”. His superpower is the ability to channel birds, a useful skill for reconnaissance.

“I think I could probably say this here in a way that makes more sense if I said it at home: he’s incredibly British, in that everything is repressed and everything is tricky and difficult for him,” he says.

Co-executive producer Daniel Kaminsky says Riley brings sincerity and warmth to the role that elevates Augie’s occasional antics and makes him a very real and interesting character.

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“A few of us had seen Tom’s earlier work and had only thought of him as a leading man, but when he auditioned for the more eccentric Augie it blew us all away – he was able to bring more to the character than what was on the page,” says Kaminsky. “He was a natural fit to our fantastic ensemble.”

The first six episodes of The Nevers are done and are showing on American pay television network HBO. The cast will return in June to finish the first season, with British screenwriter Philippa Goslett taking over as showrunner.

So secretive is the project that Riley has no idea what happens to his character. All he knows is that the world created for him is complex and with powerful themes.

“Yes, mutants have powers and they’re shunned from society and exploited. But [the show] has its eye on a bigger prize as it progresses,” he says. “It’s bolder than that. It’s more ambitious.”

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“This is the first job that I’ve done where I see people eating at lunch and I don’t know who they are, even though I’ve spent all morning for five weeks with them,” he says, laughing. “It’s been really relearning the entire experience.”

Riley studied at the London Academy of Music and Dramatic Art and his first taste of professional acting came onstage, replacing Pattinson. He’s done plays both in London and Broadway, including a 2011 revival of Tom Stoppard’s Arcadia.

On the small screen, he’s played Leonardo da Vinci in the Starz drama Da Vinci’s Demons, BBC 2’s Ill Behaviour, ITV’s Dark Heart and Amazon’s The Collection. His film credits include Starfish and Pushing Dead.

He hopes The Nevers is a hit, but he says he’s given up trying to predict what project will stick and become a career-changer.

“I’m trying to enjoy the experience more than projecting on the result more than perhaps I did in the past, which was always like, ‘Is this good? Maybe if I hold the steering wheel tighter then I’ll be better at this,’” he says. “But now I’m just happy to be in the passenger seat.”

The Nevers is available on HBO (Now TV channel 115)