GEMMA Whelan has stepped outside to talk to me. “I’m on Peckham Rye with my three-week-old son strapped to my stomach hoping that he will stay asleep while we talk. I think he will. He’s a pretty good boy.”

This is Whelan’s latest role, mum to a new baby, her second. (“Second and final,” she says. “There isn’t going to be a third.”)

But we’re here to talk about another one, as a detective in ITV’s new crime drama, The Tower which starts on Monday and is stripped across Tuesday and Wednesday.

It’s a big deal for Whelan. After years as one of the most reliable supporting actors on TV, in shows such as Game of Thrones (where she played bisexual warrior woman Yara Greyjoy), Gentleman Jack (as the conservative sister to Suranne Jones’s swaggering lesbian title character) and Killing Eve (where she turned up as Fiona Shaw’s daughter), she’s finally the lead.

“It’s supposed to be the lead,” she begins when I say as much. But she is still coming to terms with the idea, it seems.

“We were just talking about women taking the lead and not apologising for it,” she says of an earlier chat with another journalist for the Radio Times. “I just find myself always going, ‘Well, it’s an ensemble piece. There are lots of leads really. It’s a real team piece.’

“But when it comes down to it is led by me, yeah.”

She sounds almost convinced. “It was really nice to be offered my first lead for sure. That’s something everyone wants.”

The Herald:

Were you surprised, Gemma? “Either way I answer that I sound pathetic. ‘No, I wasn’t surprised,’ sounds arrogant and ‘Yes, I was surprised,’ sounds like I don’t believe in myself.

“I guess I wasn’t surprised because it was a really nice meeting. I really loved the character. I felt like I could bring something to it. It just felt like a fit. And so, I wasn’t surprised when my agent called and said it had been offered. I was utterly thrilled and then immediately thought ‘Oh my God, childcare logistics.’”

In conversation Whelan is self-deprecating as a matter of course in that peculiarly English way, playing down her talents when she’s perfectly entitled to play them up. Since she first made a splash playing her own comedy creation, socialite Chastity Butterworth, she has been jumping between comedy and drama with alacrity.

The Tower, which tackles sexism and racism in the police force, is very much at the serious end of the spectrum. It sees Whelan play DS Sarah Collins, who is assigned to investigate the deaths of two people; an experienced officer and a 15-year-old girl who appear to have fallen to their deaths from the top of a tower block in south-east London.

With a script by Patrick Harbinson, best known for his work on 24 and Homeland, and based on the novels of Kate London, what quickly becomes clear in The Tower is that DS Collins is a woman in a man’s world. And one that looks after its own.

The Herald: Gemma Whelan in Game of ThronesGemma Whelan in Game of Thrones

“It’s dealing with a lot of nuance, a lot of systemic sexism and racism, the way that we judge things, the way that we speak to each other, how we tackle events in different ways, who’s right and who’s wrong,” Whelan suggests.

And her own character might not necessarily be the best judge of such things, she admits.

“Sarah Collins’s moral compass is black and white, up and down,” Whelan admits. “There is so much room for nuance and different judgements within the police. There is no right or wrong. It’s a fantastic liquid thing to be dealing with.”

Collins is “completely wedded to her job, Whelan suggests.

“She’s not hugely successful in love and so she really throws herself into her job. She doesn’t have family to speak of and so she lives and breathes her work and doesn’t really pay attention to hours of the day. If the work needs doing, she’ll be there. She’s running away from something. Who knows what? She’s been doing it a long time, she’s good at her job and she knows she is. But it’s still very much a man’s world that she’s working in.”

As a result, she has to give as good as she gets. “I like that she’s not trying to be liked,” Whelan suggests. “I think a lot of women do try to be liked and she’s not trying to be liked at all. She’s just trying to get the job done to the best of her ability and get the best out of her team. But not everyone works the way she does. Some of them do have lives outside work.”

Even from the first episode it’s clear the limits of her position in a culture that is defiantly masculine. Machismo is still a thing in Sarah’s world. Have you found it to be the same in acting, Gemma?

“I think early on maybe yes. There was a lot more room for innuendo and things like that, things that now people would never say. What you might dismiss as ‘bantz’. If you hear any ‘bantz’ now everyone shuts down. There is not space for it anymore. It’s a great thing.

The Herald: Gemma Whelan in The TowerGemma Whelan in The Tower

“I’ve never found myself cornered by any terrible language or situation at work thankfully. I’m quite happy to hold my own or shut down or leave the room If something’s not helpful to my day. I’ve never felt threatened.”

The Tower is further proof that women are moving front and centre on our screens. They are no longer there just to support the male lead. There’s no greater example of that than the BBC drama Gentleman Jack. Whelan shot the second series of the 19th-century drama this summer just after The Tower finished filming.

“I was quite heavily pregnant by then. I wrapped in the summer before I really, really, really didn’t fit into the costume anymore.

“But isn’t it brilliant that everyone was so willing to go, ‘Who cares if you’re pregnant? Come to work. You’re not ill. You’re not an invalid. We’ll work around it.’

“I think a lot of people handle Preggers with kids gloves, but women are very tough.”

Gentleman Jack was one of TV’s most joyous dramas of recent years. It must be fun playing opposite Suranne Jones at the top of her game, I suggest. “And she’s so sexy in it, so androgynously appealing. And attractive. She’s formidable, she’s brilliant. It’s an exciting thing to watch her.”

Possibly with the exception of Yara Greyjoy, Whelan doesn’t tend to get that kind of showier role, but there’s a strength to her that deserves to be acknowledged. And not just onscreen.

In the past she has spoken about her own teenage struggle with anorexia. I wonder what it took to speak out about it.

“I think like many things in a career like this you come from a position of fear and not wanting to stop the flow of your career by introducing the fact that you’ve had mental health issues, or you’ve struggled with something,” she admits.

But things are changing.

“I think there’s a culture of sharing things in order to help each other. It is a fine line certainly. You don’t want to be oversharing. But just to say, ‘This happened. I went through it and if you are too, there is hope. You can get through it. It’s hard work, but you can.’

“I think that’s a positive thing to share with people.”

She pauses before adding, “It’s not an unusual story. I think.”

It’s worth saying that in the middle of this exchange she has to break off to talk to a friend she has just spotted. “I’m doing an interview. I’m sorry,” she tells her, before coming back to me. “I’ve seen one of my very best friends and her dog.” At which point she seamlessly returns to her point. Such professionalism.

One of the thrills of The Tower for Whelan is the chance to play a detective. She is a huge fan of true crime podcasts, as are many other women. Is it because women are more aware of just how dangerous it is to go out at night than men?

“I hadn’t even thought that true crime fans tend to be women until you just said it, but you’re absolutely right. Most of my female friends are really into it and men find it quite weird.

“I hadn’t seen it from that point of view before. It could well be. Who knows?”

We talk about the murder of Sarah Everard and how men and women reacted differently to it.

“My brother and I go for evening jogs, and so does my husband. When it happened, he didn’t think twice about still going and I thought, ‘I’m absolutely not going out,’ which I’m sure is an echo of behaviours in many households.”

In our time together Gemma Whelan tells me she’d love a career like Olivia Coleman’s. She remembers fondly her early days playing Edinburgh, but she’s not sure she could hack sharing a room with five people these days (though if the Traverse theatre needed an actor …) She’s going to film a small role in a new ITV drama in the coming weeks, but other than that she’s concentrating on being a mum.

Her son hasn’t woken up throughout our chat. “He’s still asleep and I can still see my best mate so I’m going to go and catch up with her.”

It’s shaping up to be a good day.

The Tower begins on STV on Monday night at 9pm and continues on Tuesday and Wednesday at the same time