Often when a director asks an actor if he or she can ride bareback, ski down black runs or jump out of planes without a parachute, they nod enthusiastically and panic later. When Lara Pulver was asked if she’d be happy to scuba-dive in a bikini alongside Dominic Cooper for the opening scenes of TV series Fleming, she opted for honesty as the best policy. ‘I told director Mat Whitecross that I wasn’t a confident swimmer,’ she says. ‘I don’t even like putting my head under the shower.’

Pulver put the scuba-diving to the back of her mind, engrossing herself instead in the script, which is set against the backdrop of World War II and follows the story of Bond creator Ian Fleming and his wife, Anne O’Neill, played by Pulver: ‘My immediate response was, she’s fun and tragic. Then Mat sent over her diaries and I sat there for four days, reading and making notes. I’ve never been so engrossed in someone’s life. Her mother died when she was young, she had an abusive nanny, she was passed around the family. I could totally see why she became addicted to her dysfunctional, sadistic relationship with Fleming.’

Eventually, Pulver found herself flying to Mallorca, which was to double as Jamaica, where Fleming built the Goldeneye estate. She spent part of the day at a diving centre with Cooper and convinced herself she couldn’t do the scene. That evening, her partner Raza Jaffrey (also an actor; they were both in Spooks) suggested on FaceTime that she fill the bathroom sink with water and repeatedly dunk her face in it. Daft as it seems, it worked. The next day, she did the scuba-diving scenes. She is still exhilarated now: ‘I hate admitting defeat and I didn’t have to!’

Pulver, 33, is certainly not one to linger inside her comfort zone – something that makes her not only a bold actress but one to watch. She started her career working in the theatre, and five years ago was nominated for an Olivier Award for Best Actress for her role in Parade at the Donmar Warehouse. Recently, she filmed a small cameo with Tom Cruise for the upcoming Edge of Tomorrow (‘I was rather in awe of him, in a healthy way’), yet it was a Brit TV show that made her name.

Pulver is still probably most famous for that scene in Sherlock where, as dominatrix Irene Adler, she got naked in front of Benedict Cumberbatch. Though it lasted less than two minutes, it became an overnight YouTube hit: ‘I remember doing the ADR [additional dialogue recording] for that scene and never for a second did I think it would become “the nude scene from Sherlock”. I think we have a problem if that’s what people take from one of the most intelligent and challenging British TV shows.’

She takes a sip of her peppermint tea and continues: ‘Benedict had just done Danny Boyle’s Frankenstein at the National, where he was naked every other night as the Creature. He said to me straight away, “I know what it’s like to be butt naked in front of an audience.

Just so you know, I will never look below your eyeline. I will not disrespect you in that way.” He was so courteous. A total gentleman.’

Very little is yet known about the third series of the phenomenally successful Sherlock, other than that its protagonist is still alive despite appearing to leap to his death at the end of the second series. Pulver admits that Adler is in the new series. But all she can say is that ‘it’s a gift to play such a powerful woman’ – and that she’d love to play another alpha female or co-write a script with women at its centre.

Based in Los Angeles with fellow Brit Jaffrey, she spends months at a time working in Wales shooting a British-American TV series. ‘Da Vinci’s Demons is a big deal in the States,’ she explains. ‘But no one really knows about the show here. It’s a little odd playing a Renaissance wife in Swansea for an American show. But Steven Moffat [co-creator of Sherlock] was down the road working on the Christmas episode of Doctor Who, so it felt like a little Welsh family.’

Soon Pulver will fly back to LA, where she says she will be cleaning out kitchen cupboards. ‘I thrive on being pretty grounded, which is useful because being an actor is pretty surreal. Quite a few years ago, in my twenties, I realised that I wanted to act, but that I didn’t need to. It was hugely liberating, meaning I could ultimately step away from it and be okay.’ Fleming will be shown on Sky Atlantic HD in January; Sherlock airs on BBC One in 2014