Belfast-born Donnelly plays lead character Amalia True, a mysterious woman running an orphanage for people (mostly women and girls) who, like her, are Touched — gifted/cursed with supernatural powers. These abilities are known as Turns and include superhuman strength, clairvoyance, the ability to control fire and the power to turn objects into glass. No two members of the Touched have the same Turns. It’s sort of like someone mixed up X-Men, Sherlock Holmes and that whole steampunk/Victoriana vibe into a funny, exciting adventure.

The show looks fantastic and is enjoyable to watch — and, according to Donnelly, it was just as much fun to make. “It’s been my favourite screen experience of my whole career, for sure,” she says. “Amazing cast and crew, brilliant script, and I just love this character. I want to do much more of it and her. I’d play this character forever.

“Walking on set, you really do have to pinch yourself — that you’re there, in this fantastical world. I’m glad I took the time, at many points during the shoot, to remind myself, never take this for granted. As an actor, you don’t know what the future holds, how long you’ll be doing this, when you’ll next get a job like this that ticks every single box you want it to tick. So many times I told myself, just remember that this is not normal. Don’t get used to it. When you do that, you stop being grateful.”

The Nevers is released in full on May 17 on Sky Atlantic and the Now streaming service. It has just aired Stateside to good reviews and HBO Max’s biggest premiere audience ever.

The producers originally planned a first season of 10 episodes. Covid interruptions forced a rejig: it was has been into two parts of six shows, with “Season 1B” due to start filming soon.

“Reaction has been brilliant, we’re thrilled,” Donnelly says. “And audiences enjoying it means hopefully we’ll get back for a second or third season. This is the biggest show I’ve been involved with by a long way, so it’s really exciting. We worked very hard on this for the last two years, hundreds of people giving blood, sweat and tears. We’re all so proud of it and really believed in it. Now the fact that finally it’s here, after complications with Covid and all the rest, is so gratifying. At last people are getting to see what we’re doing.”

She jokes that this feels something like a parent presenting a child to the world. Positive social media reaction was “lovely”, with people getting in touch “to say how much they’ve been enjoying it”.

“Of course as an actor you try not to be dependent on the outcome — to just enjoy the work itself as best you can — but then if other people like it, you get to do more of that work,” she says.

Her character, Amalia, is ambiguous. When we meet her, she seems to be trying to drown. A few minutes (and three fictional years) later, she is the calm, resilient and somehow inscrutable de facto leader of a “new evolution” in humanity.

“There’s a lot that’s unspoken at the beginning,” she says. “There’s a big backstory, a lot going on, and that was one of the primary things that drew me to the character, those layers. I got to figure out what to reveal and not reveal, even to herself. What is she aware of, about herself? What is she burying inside? Those things make preparing a character so much fun; you get to make some real choices.”

One of the keenest pleasures of The Nevers is Donnelly’s fizzing interactions with the young Dublin actress Ann Skelly, who plays Penance: a scientific whizz-kid and basically Amalia’s aide-de-camp. There’s a real Batman and Robin — better yet, Holmes and Watson — vibe to their relationship.

“I love Ann. She’s rapidly becoming one of my favourite people on the planet,” Donnelly says. “She’s such a good actress and we bonded really quickly. We had a ‘chemistry read’ together, before either was officially cast, and the moment she stepped into the room it was like, ‘Oh we’re both Irish, great’.

“We got very close very fast. I think a lot of that is because we’re not dissimilar to our characters, and the dynamic between us in real-life isn’t dissimilar either. She’s the warmest, funniest person. She feels like a true support and brings out the best in me, and I think she’d say the same. We really enjoy acting together. I feel I do a lot of my best work when I’m in a scene with Ann.”

The 38-year-old has assembled an impressive resumé — including TV hits such as The Fall, Outlander and Britannia, and the 2019 film Tolkien — but it’s perhaps in theatre where her star has shone most brightly.

Trained at the Royal Scottish Academy of Music and Drama, Donnelly has done Shakespeare, Brian Friel and a raft of modern plays, including The Ferryman (written by her husband Jez Butterworth) and the avant-garde Tutto Bene Mamma? She’s been directed on Broadway by Oscar-winner Sam Mendes, acted on Broadway opposite megastar Hugh Jackman and won the prestigious Olivier Award and been nominated for a Tony.

It all began with childhood acting experiences, “falling in love with the stage and making me want to be an actor”. Her first job after college was a play at the Project Arts Centre in Dublin. She “quickly” went to TV as well, describing it now as her second home. It’s clear that she finds stage and screen equally important.

“I knew early on that I wanted to combine the two,” she says. “I get different things from them. They’re very different artforms, for audience and actors, and I truly enjoy both. Any time I finish a long run of a play, I’m dying to get in front of the camera, and vice-versa. I love the variety.”

Donnelly is mostly based in London, where The Nevers was made. Life, she says, has “settled down” in the last few years. Before this shoot, she would spent six months a year in New York; back when she was starting out there was “a lot more moving around”.

She would go to California and work in pilot season, travel around for auditions. “As my career has progressed, I haven’t had to do that so much,” she says. “And of course technology has changed things. I do slightly miss the nomadic lifestyle, but there’s a lot to satisfy me too. I have no complaints. And I have a couple of kids now, so it’s not practical to be rushing off.”

Acting, she admits, remains a mystery — in a good way. “You can do all the prep and research and decisions on where to go within a scene,” Donnelly says, “but there’s a part of it ultimately that I can only put towards inspiration. Every time you walk on set, it’s a bit of a Hail Mary. You’re hoping the magic is there and don’t always know if it can be harnessed. But that mystery is part of what I love about it.”

‘The Nevers’ begins on Sky Atlantic at 10.10pm May 17 and on the Now streaming service