After spotting a handsome police officer she likes the look of, she demands to be introduced – and then purposefully tells him which hotel room she is staying in.
It’s a far cry from prim FBI agent Dana Scully, who spent years in The X-Files refusing to get too close to her partner Fox Mulder (David Duchovny) before she finally gave in to her feelings. “When I’ve been asked about the differences between the two of them, suddenly it occurred to me that Scully was quite square,” says Anderson, 44. “She was quite prudish and always behaved correctly and wouldn’t necessarily be wearing lace panties. In comparison, Stella is quite comfortable with herself, comfortable in her skin, is a lot more feminine than Scully ever was.
“For a long time, Scully felt quite childlike, and part of that was because I was a child when I started to play her and audiences got to see me grow up and grow into her. But whenever I see her, she seems like a 12-year-old pretending to be an agent.”
Stella isn’t the only sexual predator in The Fall. The eerie new BBC crime drama, set in Belfast, is the story of a serial killer, played by the devastatingly handsome Jamie Dornan.
The audience know Dornan’s character for what he is from the beginning, while Stella is the investigating officer trying to pin down her man.
It’s so spookily shot that viewers are often left feeling like voyeurs. As well as watching Dornan’s victims, we see Stella alone, reading in bed, cleaning her bath and swimming – which is her escape from the unpleasantness of her job.
“I’m actually not a swimmer. I don’t like water that much,” confesses Anderson. “I thought I was going to tire of it. But I enjoyed it. I actually thought I should start swimming, but I didn’t …”
She seems more comfortable with the sex scenes than the swimming. “There are always funny moments in sex scenes, just with all the tension and bits falling off and not protecting you properly,” she laughs. “They get very, very serious because they’re very technical and both parties get undoubtedly nervous.”
The steely detective keeps people at a distance, gives little away and is completely focused on her work, munching an enormous burger while she looks at evidence photos of dead bodies on her laptop.
“I love how you don’t really get to know who she is or what makes her tick, and yet you want to know,” says Anderson.
The Chicago-born actress admits she is keen on Prime Suspect, the award-winning crime drama that starred Dame Helen Mirren as the hard-as-nails DCI Jane Tennison.
“I was always a fan of Prime Suspect and had read other attempts at recreating that and always found them lacking. And there is something about this that felt like it had the depth and complexity, and yet simplicity, of that series.
“The thing I found really fascinating about Tennison, she was quite self-centred and certainly had ego.”
The Fall was shot on location in Belfast, but Anderson admits she didn’t see much of the city and didn’t socialise much with the rest of the cast.
“I am a bit of hermit anyway,” she says. “But I become more of a hermit when I’m working and even if I have a few days off I generally just stay in my hotel room.
“I don’t know if that’s necessarily keeping in character, it’s more keeping my mind on it.
“I’ve worked with actors who keep in character all the time and I don’t do that,” she adds with a telling sigh.
Anderson has been divorced twice and has a teenage daughter from her first marriage and two young sons, aged six and five, from her second.
She spent her early childhood in London while her father, a film producer, attended the London Film School.
Around the time The X-Files ended in 2002 she moved back to Britain, where she has chosen to live and bring up her family. She has continued to act over here, appearing in British television shows including Great Expectations, The Crimson Petal And The White and Bleak House, and has been nominated for several TV Baftas.
But back in the US it has been hard to shake off the ghost of Scully. “Whenever I do go back, there might be some who know I do other things, but the fact is, how much of this stuff airs for the masses?
“I get people going, ‘So what have you been up to?’ I’m not really on the big screen over there and a lot of the small screen things they might not have seen.”
Anderson is appearing in new US crime drama Hannibal which stars Mads Mikkelsen as Dr Hannibal Lecter. “They’re selling it as my return to television after ten years away!” she exclaims.
But with a young family in the UK, Anderson has to both support them and be there for them. “Schedule is everything,” she declares.
“I’m very picky about dates and the kids are the most important thing. If it’s something I want to do but it takes too much time away, then I’ll decide not to.”
She also admits she’s extremely choosy about the type of scripts she’ll accept. “My daughter always says, ‘God mum!’ Game Of Thrones, Downton Abbey or whatever it is. She cannot believe I’ve turned things down that she loves to watch.
“But if I’m going to spend that amount of time then I’d prefer to be working with Scorsese, do you know what I mean?”
Anderson has always been wise with her selections, and it would be no surprise if Stella Gibbons becomes an iconic detective – like Jane Tennison and Dana Scully.
She hopes the show will be recommissioned, noting: “We’ve been told it looks good.”
Does she want to play Stella again? “Yes definitely,” she breathes nervously, and quickly changes the subject, wary of jinxing the role she has already taken to her heart.
• The Fall begins on BBC 1 next Monday, 13 May