Broadchurch, who? The Fall is our new TV obsession. Gillian Anderson and Jamie Dornan’s police officer/serial killer dynamic is the most thrilling thing on screens this summer. We’re hooked.

Gillian Anderson is a great actress. She must be, because there is absolutely no way she could possibly be as calm and collected as she appears to be, while being picked up and swung around by a man so incredibly handsome, it is almost absurd.

If she is having the same teenage palpitations as the rest of the Red photoshoot crew in her co-star Jamie Dornan’s presence, then for God’s sake, someone give this woman an Oscar because, honestly, you would never know.

It is late on a Monday afternoon, and Anderson (who needs no introduction to anyone who owned a television in the 1990s) and Dornan (who you might need to Google but, when you see the Calvin Klein shots from his modelling days, all oiled and astride Eva Mendes, you won’t regret the task) are here to talk about The Fall. It’s a dark, gripping, brilliant BBC drama, in which Anderson plays DSI Stella Gibson, a police officer in the Jane Tennison vein, while Dornan plays Paul Spector, a serial killer unleashing hell on the streets of Belfast. The casting is spot on. For Anderson, it’s a welcome return to TV after nine years as The X Files’ Dana Scully, via the BBC’s Great Expectations and a Bafta-winning role in Channel 4’s Any Human Heart. For Dornan, it’s by far his biggest and most complex role to date.

‘You do read so much shit,’ Dornan laughs, post-shoot, of the roles he has been offered in the past. ‘I don’t know if I particularly get sent more than other people, and some of that might have to do with the fact that I modelled, but very often I get pushed towards a similar type of role. Usually it’s the character that, two pages before the end, kisses a girl and that’s that. It’s so rare that a character this good would even be an option for me. I didn’t think I’d have a chance in hell of playing Spector. I’ve never been on British television before, so for my first thing to be something as good as this…’

‘Yeah, they made you jump through some hoops,’ Anderson adds, from her seat next to him on a huge leather sofa. ‘But I think it was pretty clear from the beginning that you were the man for the job. I just think it was a matter of convincing the powers that be. I’ve been in the same situation before, with people fighting my corner, but having to convince studios that you’re the one – it takes some effort.’

They may have very little screen time together – as the hunter and the hunted, they play a continual game of cat and mouse – but the bond between the two is easy. They joke around on set while, during our interview, it’s more of a conversation between the two of them than an interview for me, with Anderson offering Dornan advice, and him taking in every piece. For both actors, this show seems to be an important moment in their careers.

‘I think Stella is probably one of my favourite characters I’ve played,’ says Anderson, 44, in her transatlantic lilt, a blend of the British accent from her formative years living in London, with the American one picked up from years living Stateside.

She now, once again, lives in London, with her three children – Piper, 18, Oscar, six, and Felix, four. ‘I haven’t figured out how to say this without it sounding bad, but I feel like Stella is closer to me than anybody I’ve played before.’ She pauses, before bursting out laughing, adding, ‘It’s just I usually say that after I say I think she’s really cool.’

‘Wow,’ Dornan deadpans, joining in the laughter.

‘I know! It doesn’t come out so good,’ Anderson grimaces. ‘But I really like her as a woman, I like her more as a woman than me. I think there’s something really cool about her.’

For Dornan, 31, The Fall is something of a breakthrough. After years of modelling, with Calvin Klein billboards plastered across every major city in the world, and campaigns for Asprey, where he met one-time girlfriend Keira Knightley, convincing people to take him seriously as an actor has been no easy ride. His biggest role to date has been in the US series Once Upon A Time, but British roles have been trickier to secure for the Northern Irish actor.

‘Modelling doesn’t hold you back in LA at all,’ he says, with characteristic honesty. ‘In LA, they don’t think that because you leant against walls and looked depressed while someone took your photograph, it means you can’t act. In the UK, there’s a massive stigma attached to it. You couldn’t possibly have had your photograph taken for a living and act.’

‘It’s so weird, because my experience is completely opposite,’ Anderson tells him. ‘When I first moved here, I was offered Bleak House, which was so different to anything I’d ever done before. Not in a million years would I have got a role like that in the States. There was a belief here that, even though I’d done Scully, I could do period drama, too. I wanted to say to them, “Why do you think I can do this?”’

‘But Scully is a really fucking interesting character, in a massive show, and you’re really impressive in it,’ replies Dornan, emphatically. ‘So that’s nine years of constantly being impressive as an actress, whereas I’ve got nine years of leaning against walls – and it treated me very well, but it was almost to my detriment as an actor.’

‘It’s just going to take a couple of things like this and that will change,’ Anderson offers, warmly, of the transition from model to actor. While they are both clearly very proud of the show, filming in Belfast for three months was not an easy decision for Anderson, who, as a single mother (she separated from husband Mark Griffiths last year), tries not to be away from her London home as much as possible.

‘It’s all timing and scheduling and what I’m in the mood for,’ she says of her career choices. ‘For me, everything is about schedules. But with this, once I recognised that I had fallen in love with it and was determined to make it work, there were ways to compromise. It’s also about choosing things I don’t feel like I’ve ever done before. I see actors who have done 60 films that are the same and I think, how do you even show up any more? If I sense I’m doing something I’ve done before, it drives me insane.’

Did Dornan show her round his native Belfast?

‘No…’

‘You were never there! You’d sneak off back to London,’ he laughs.

‘Yeah, on weekends I’d come back,’ she admits. ‘And usually, generally when I’m working, if I’m not on set, I’m in my hotel room.’

‘For me, it was a very different experience,’ says Dornan. ‘My dad’s there, some of my best friends in the world are there. I had an apartment in the middle of town for three months. And I’ve never actually lived in Belfast because I grew up just outside, so I experienced the city on a different level, waking up and going to get coffee and read the papers on my day off. I’d never done that, so I just loved it. And it’s nice to not have to repeat yourself, as well, in terms of your accent!’

With easy laughter, and gentle teasing, it’s obvious that pairing these two together was a genius move. They chat happily about Dornan’s upcoming wedding to singer Amelia Warner (they marry four days after our shoot), the experienced, worldly-wise actress, and her younger, greener co-star.

What is the most important lesson each has learnt? ‘To have no expectations,’ Anderson says, immediately. ‘I’ve done things I’ve thought were going to be the thing, and then they’re really wrong; and things I’ve thought were potentially going to be a bit mediocre, and have turned out to be not so.’

‘I think my lesson is to back yourself once you’ve been given a job,’ says Dornan. ‘Far too often, I’ve been given a job and then doubted why I’m there. I’ll assume they’ve made a wrong decision. I felt a lot of pressure when I first started filming this, because there was no denying that it was a risk to cast me. I doubted myself for at least the first two days.’

‘I feel that in every new job I go to,’ Anderson tells him, reassuringly. ‘The first couple of days, I think I’m going to be fired, I really do. Generally what happens for me, and it happens all the time, my first day is the divorce scene or the death scene.

I just did a pilot for NBC (Hannibal) and every single difficult scene was on the first day. I was thinking, this is all going to end up on the cutting-room floor and they’re going to recast.’

The self-doubt that each actor feels, I can quite confidently say, will not translate to audiences. As a serial killer by night and loving family man by day, Dornan is compelling, terrifying and brilliant, while Anderson sets the bar high for a new breed of strong female TV characters. There is already talk of a second series – and frankly, I, for one, cannot wait.