THERE is a very simple reason why Emily Beecham knows her profile is on the up these days. The scripts are getting better. “It’s no longer ‘girl who jumps into a river in a bikini and gets eaten by piranhas,’” she tells me over coffee and almond milk. “That happened to me once. Nobody wants to see me in a bikini.”

A Friday morning in June at the Edinburgh International Film Festival and no bikinis in sight. (I was thinking of wearing mine, but it’s clouded over …)

Beecham, 33, has caught the red-eye flight from London to support her new film Daphne, which is getting its UK premiere at the Film Festival. A few days from now she will pick up the festival award for “Best Performance in a Feature” as the title character. And rightly so. Because Beecham quite frankly burns up the screen as a cynical, difficult, exasperating chef at large in London, all red hair and bad attitude.

In the film Daphne spends her nights drinking and propositioning men and her days sniping at her ill mother (played by Geraldine James). Glaswegian director Peter Mackie Burn’s queasily impressive character study – his first full-length film – is a small, intimate thing, but Beecham makes a huge impact in it.

If you haven’t noticed Beecham before – perhaps in a small role in the Coen Brothers’ last movie Hail Caesar, or in the corsets-and-Kung Fu American TV drama Into The Badlands – you will start to take notice from now on. Beecham’s performance in Daphne is so good it should mean the bikini-and-piranha scripts never darken her doormat again. She’s a force of nature here, a vision of a selfish, self-destructive young woman burning bridges at every turn.

If anything, this morning the memory of her performance overshadows the woman in front of me. “I need to wake my brain up,” Beecham admits when the coffee arrives. But once she does the actor behind the role emerges as spirited and opinionated in her own way.

The question, Emily, I ask, is do you like Daphne? “Some people don’t,” Beecham admits. The comparison she reaches for is Phoebe Waller-Bridge’s recent BBC sitcom Fleabag (the one about the snarky, outspoken, broken young woman with a traumatic back story).

As with Fleabag, some people, Beecham admits, simply won’t warm to Daphne. “'Why is this person deserving of being on a screen? This person is unpleasant.’”

But that’s just some, she says. “Other people really love her for her candid honesty and I think a lot of people relate to her. I relate to lots of parts of her and I see a lot of friends that I know in Daphne. And that’s not really represented on screen very often at all.

“I read a lot of women roles and an awful lot of the time they’re ‘girlfriend’ roles. They’re facilitating this thing and you’ve got to go in and be charming, loveable and adorable … Oh God,” she moans. “But the really brilliant roles are the ones in which your character can have many flaws and is not just there to decorate the screen.”

If anything, Beecham adds, she was rather sad to leave Daphne at the end of the shoot, because the character seemed so real to her. “She’s railing against what’s expected of her and now we’re in an age where women are settling down later and she’s very independent and she’s questioning. She’s a little bit nomadic and as an actor I can relate to that.

“But many people have the same experience. And then there are all these expectations from society. You’re contending with what you’re being told about how you should look and all these expectations.”

Of course, being judged on her appearance is surely rather inevitable given Beecham's career choice? “Well, yeah, but you can’t really care about that sort of stuff if you want to do good work. I feel it hinders you doing interesting things.”

Daphne definitely qualifies. What was the part of the character that was furthest away from the actor then? “Uh, probably wanting to work in a kitchen. I don’t think I would manage that very well at all. I think I would flounder.”

Did you have to do your time in a kitchen though to get a flavour of it? “Yeah, but they didn’t trust me with the busy hours. They didn’t trust me with the really important stuff. I did a lot of chopping and cleaning and being around the kitchens. But they didn’t let me participate too much in case I might poison someone.”

In another life Emily Beecham might have been an artist. She had the chance to go to art school before opting for drama school, and over the last few years she’s picked up her brush again. What does she paint? “Abstract sh**, really.”

Painting also offers some stability, she suggests. Stability may well be the thing she has sacrificed for her career choice. Painting and reading, offer “a bit of calm”, she says. “And staying in one place.

“But then I love travelling to different places.”

If actors are natural nomads then maybe Beecham, who studied at the London Academy of Music and Dramatic Art (Lamda) and picked up an agent after a showcase, was fated to be one. Born in Manchester, she moved around a lot as a child because her father was a pilot. Her parents themselves were a transatlantic co-operative. “My mum’s American. I spent a fair bit of time there but I grew up here. I lived in Glasgow for six months when I was very young. I can barely remember it though.”

Her American heritage had its own downsides in the UK. “I noticed quite a bit of prejudice actually. I had a lot of school friends telling me they didn’t like Americans and I think that probably taught me a lot. I was like: ‘Have you been there? Do you know any Americans? We’re all very different. We’re not all represented by our governments.’

“And my mother is also very open and forward and I know those are often American qualities.”

Does she take after her mother? “I think so, yeah. I always did like communicating with people and I think that maybe did influence my decision to do acting. I really like communication and I really hate a repressive environment. I love watching theatre because it turns everything inside out. It exposes everything. It exposes relationship dynamics and that always really excited me. I just like honesty.”

Growing up, it was her mother who would accompany Beecham to the theatre. “She took me to see The Blue Room probably when I was inappropriately young.”

Well indeed. David Hare’s play – an adaptation of an Arthur Schnitzler work better known by its French title La Ronde – is best remembered for Nicole Kidman’s brief nude scene and a heated Telegraph review which described the result as “pure theatrical Viagra”.

“There’s an oral sex scene,” Beecham recalls, “and I was completely, utterly mortified. But I loved the experience of watching theatre. It’s telling truth. Really.”

Truth and honesty are clearly buzzwords for Beecham. But sometimes acting is a form of play. That’s surely the case with her biggest success prior to Daphne. The American post-apocalyptic cable drama Into The Badlands – now onto series three – is by far the biggest. Shown on AMC (home, also, to The Walking Dead), Badlands is, she admits, the “polar opposite” of Daphne.

“The scale of these shows is much bigger. It’s massive, which is exciting, because you then have the budget to create a really excellent show and a whole world.”

That’s the advantage of a blockbuster TV series. But there are advantages too. “For a big network show they’re always thinking about the ratings. It’s a money thing. So there’s always that pressure. You never get to discuss things. You just have to do it. It’s very commercial.”

Presumably, there’s martial arts boot camp training required. “Oh gosh,” she nods, “it was so extreme. First season we did five-week training. From zero to 100, doing about six hours martial arts with a Hong Kong fight crew who have been doing it since they were practically six years old. They’re athletes.

“I saw my body changing, which is very strange. I had muscles appearing in places I’d never seen them.”

And presumably you need to maintain that level of fitness through the shoot? “We do. It’s a challenge because we’re on set six days a week in a corset and big hair, massive costumes. I can’t exactly do push-ups or yoga in it at all. I can barely sit in it.”

What are the scariest stunts? “The heights. The harnesses. They don’t choreograph the shows. We get onto the set and they break it up into sections. They’ll show us like six fight moves and we block it through and we’ll run it about two or three times and then we’ll do it. They’ll be like: ‘Lots of energy, Emily. Really tough. Really tough.’

“I had to jump off a balcony that was three storeys high on a harness. And it’s held by two guys who only speak Chinese. There is a kind of translator but it’s so loud that communication is really difficult, so I’m crapping myself a bit. I can handle the heights, but the unrehearsed heights …”

Has she any scars from all this? “I almost broke my nose actually. I had to stop filming because I looked a bit different with my swollen nose. It’s very guerilla style.”

This is all rather far away from Daphne, you might think, never mind Beecham's dream gig of working with Mike Leigh. (“He really understands the acting process and he really listens to you.”)

But you could also see it as physical expression of her mental strength. Because it’s not just on set that Beecham has had to be “really tough”. She has already rejected some of the pressures of her chosen career.

“I used to have my old American manager who I’m not with any more. He was giving me feedback: ‘You have to look prettier. Put more make-up on for these tapes,’ blah-di-blah.

“And after a while I thought: ‘Sod this. I don’t want to take that abuse any more.’ And now I have a new manager and I was really honest with her. I said I only want to go up for things that you think I’m actually right for the way I am and the way I look.”

Harnesses aside, Emily Beecham has taken control. Daphne, a vision of an out-of-control young woman, is only the latest example of that. Tough enough? It turns out that Emily Beecham may well be. Frankly, I am not sure the piranhas would have stood a chance, quite frankly.

Daphne opens in selected cinemas on Friday. The film’s director Peter Mackie Burns talks about making his first feature film at the age of 49 in tomorrow’s Herald