The second cycle of The Hollow Crown, the BBC’s epic adaptation of Shakespeare’s history plays, covers the Wars of the Roses, encompassing the Henry VI trilogy and its better-known appendix Richard III; reframing them, gloriously and gorily, for a Game of Thrones generation unfazed by the sight of soldiers playing catch with severed heads.

A key figure in the last stages of the cycle is Elizabeth Woodville, the Lancastrian widow whose beauty so entranced Edward IV that he married her despite her “commoner” status. She bore the king ten children, among them the Princes in the Tower — Richard, Duke of York and Edward V. Her complex relationship with her murderous brother-in-law, Richard III, has puzzled historians, not to mention novelists from Josephine Tey to Philippa Gregory, whose 2009 novel about Elizabeth, The White Queen, was itself adapted for TV.

This complexity is water off a duck’s back to Keeley Hawes, who plays Elizabeth fresh from her twin triumphs as DI Lindsay Denton in Line of Duty and Mrs Durrell in The Durrells. Watching Hawes’s gracious, intelligent performance as part of an ensemble that includes Benedict Cumberbatch and Judi Dench, you would never guess that it was the first time in a career spanning 20 years that she had attempted Shakespeare.

And yet that is genuinely the case, the actress admits, folding herself into an armchair in the lounge of a hotel in Richmond, southwest London, not far from where she lives with her three children and husband, the fellow actor Matthew Macfadyen. “I was sent the scripts and immediately I said, ‘No, I can’t do it and I don’t want to embarrass myself trying.’ I didn’t grow up reading Shakespeare. I never read it at school. But my agent persuaded me to have a chat with [the director] Dominic Cooke and slowly I warmed to the idea. I thought, ‘Well, if I’m going to do Shakespeare for the first time at my age, I might as well do it with Judi Dench. What’s the worst that can happen?’ ” The long, flowing Robin Hood-type costumes had their advantages — “You could keep your jeans on underneath if it was cold” — but overall she found the experience tough. It didn’t help that her first scene was a long one, filmed in a single take, opposite the more experienced Cumberbatch playing Richard III. “It was one of the hardest things I’ve ever done, definitely. Like learning a new language — as extreme as that. I really worried about it and worked really hard at it. But then we started rehearsing and it became clear that everyone, even Judi — and if anyone knows anything about Shakespeare, it’s her — has to pick through it and work it out. That was such a huge relief to me. I’d felt almost like there was a secret society of actors and people who enjoy Shakespeare and understand it and like it. And I wasn’t part of it.”

The daughter of a cabbie, Hawes grew up in a council flat in Marylebone — she has elocution lessons to thank for her crisp, BBC accent, which seems to have stuck and become her “normal” voice. A grant enabled her to attend the Sylvia Young theatre school, where one of her classmates was Emma “Baby Spice” Bunton. Its focus, though, was West End musicals rather than traditional theatre: there was no Shakespeare on the curriculum.

Do upper-middle-class actors have an advantage when it comes to breaking into Shakespearean acting? “Well, yes. I was never taken to the theatre when I was growing up. My nan took me to Dancing On Ice once a year. Theatre’s not at the top of the list for working-class families.”

She stresses the value of school trips to the theatre and is, like many actors, worried by the new GCSE drama syllabuses that no longer require pupils to watch a live performance. (They can analyse a streamed one instead.) “It’s extraordinary and ludicrous — like studying to be a writer and not being allowed to read. I mean, streaming is great — not everyone can fly in from Japan to see Benedict’s Hamlet — but it has obvious limitations. And it’s the poorer kids who suffer.”

I wonder if her cultural aspirations set her apart within her family?

“No, but I mixed with people at stage school who I wouldn’t have mixed with had I gone to my local state school. There were people at Sylvia Young from all walks of life and all areas of the country, so that broadened my horizons. One of my clearest childhood memories is of being taken by a friend’s family to the opera and to a Chinese restaurant, both on the same night!” She laughs her full-throated, infectious laugh. “I hadn’t known places like the Royal Opera House existed. The Chinese meal was an eye-opener too.”

For now, Hawes is relishing the pleasure viewers (eight million of them) are taking in Simon Nye’s deft, PG-filthy My Family and Other Animals reboot The Durrells — “just a joy to film”. Another series has been commissioned — and of course there’s Jed Mercurio’s serial shockathon Line of Duty.

Somehow, her return as glowering, volatile Denton in series three was kept a secret. Hawes can’t believe no one blabbed. “It’s extraordinary when you think about the number of actors involved in, say, the courtroom scenes, and the fact that we were out and about filming in Belfast. I kept thinking, ‘It’s going to come out, it’s going to come out — one of the tabloids will have it.’ What the producers threatened people with, I don’t know.”

Denton has been career-changing for Hawes. Unable, because of the nature of the character, to use her looks or talent for comedy as a shield, she delved deep into who knows where to forge a sympathetic monster for our times. Suddenly, and at an age when many actresses are worrying about work drying up, Hawes is being offered parts she says she would never have been offered before — Elizabeth in The Hollow Crown; the lingerie shop owner Samantha in The Casual Vacancy; and, most recently, the mother of an abducted child in the much-anticipated second series of The Missing, which reunites her with her former Our Mutual Friend co-star David Morrissey.

In February, Hawes turned 40 — that arbitrary milestone for female actors. “Yes. After that, if you go down the route of having work done you’re ‘fighting back the years’, but if you don’t you’re ‘letting yourself go’.” She sighs. “I look at Judi Dench and Meryl Streep — at their faces and their careers — and that answers the plastic surgery question for me.”

She and Macfadyen lead as normal a life as their competing schedules allow — “Things seem to fall roughly, with very blurry edges, that he’ll do something and then I’ll do something” — and suffer tabloid intrusion only occasionally. “I’m not held up or ridiculed for not being a stick insect. Yes, there have been pictures of me eating burgers at fêtes. But you know what? I eat burgers at fêtes! What am I supposed to do? Sit around waiting to be seen eating lettuce? That’s not what I am. Besides, it’s joyful, isn’t it, having a burger at a fête?”

A few weeks ago, a journalist asked Hawes if she was surprised by the success of Line of Duty. Not really, she said. “And I added, as a joke — as a joke — ‘I always knew I was good.’ Now, I worked with a photographer once when I was very young and he said, ‘Bit of advice for you: never smile with your teeth.’ As a result I’ve spent the last 20 years smiling with my mouth shut, which pushes my cheeks up and can make me look smug, like the cat that got the cream. So what did they do? They put one of these photos on the cover with the strapline ‘Keeley Hawes: I always knew I was good’! I mean . . .” She puts her head in her hands. “My 16-year-old son [from her first marriage, to cartoonist Spencer McCallum] was staying with his grandparents. He called me and said, ‘Mum, I’ve just seen something really weird.’ I said, what? What have you seen? He said, ‘You, making this smug, cat-that-got-the-cream face and underneath it says, I always knew I was good. What’s going on?’ I was like, no, no, no . . . What actor would say something like that seriously?”

I can think of several, I say. But Hawes disagrees.

“No actor I know would say that. Most of us have no confidence whatsoever. And to put it on the cover!” She makes her “Denton face” and for a few seconds the room temperature dips. “I’d really like to have a word with the person who did that . . .”

The Hollow Crown: The Wars of the Roses begins on BBC Two on May 7