Let us pause to recall iconic movie kisses: Burt Lancaster and Deborah Kerr, limbs entangled on the beach in From Here to Eternity. A rain-soaked Audrey Hepburn and George Peppard in Breakfast at Tiffany’s. The spaghetti-fuelled lip lock in Lady and the Tramp. That spine-tingling upside-down kiss in Spider-Man. A coming-of-age smooch between Harry Potter’s Daniel Radcliffe and Katie Leung.

Leung was only 16 when she landed the part of Cho Chang in the record-breaking movie franchise based on JK Rowling’s books. The Motherwell-based teenager auditioned after her father spotted an advert for the Harry Potter and the Goblet of Fire casting call. Leung was selected from more than 3,000 hopefuls and catapulted to stardom.

Fast forward to the present day and Leung sits in a Glasgow hotel looking adorably like a fawn caught in the headlights. Whatever I was expecting of a young woman who found global fame in her teens, it certainly wasn’t this. Starry, perhaps. Ostentatious. Prickly, even. Yet Leung is none of the above.

She had tiptoed shyly into the room a few moments earlier, apologising profusely for her dressed-down attire amid the opulent surroundings of Hotel du Vin at One Devonshire Gardens. Cute as a button, Leung appears far younger than her 28 years. She has an open, expressive face and animated eyebrows that shoot up like exclamation points as she speaks.

“I was so innocent and naive,” she muses, reflecting on that pivotal early role opposite fellow Hogwarts alumnus Radcliffe. “I think that allowed me to enjoy the moment of being a teenager, part of this massive franchise and not really having a worry in the world. If I was given the chance to go back and relive it, I would probably try to absorb everything around me a bit more.”

A decade has passed since Cho Chang kissed Harry. In the intervening years, Leung has completed two degrees (in photography and drama) and racked up a raft of envelope-pushing roles including that of an illegal Chinese immigrant in Channel 4 series Run and most recently a stint playing a North Korean defector in You for Me for You at the Royal Court Theatre in London.

Leung will next grace our screens in BBC drama One Child, which airs this week. In a trio of one-hour episodes, she plays the lead, Mei Ashley, an astrophysics student living in London who was adopted as a baby from a Chinese orphanage by a British-American couple.

Out of the blue, Mei gets a message that her birth mother, whom she has never met, urgently needs help. Mei’s brother has been wrongly accused of murder and faces the death penalty. The powerful tale is set in Guangzhou under the shadow of China’s controversial one-child policy.

The brutal population control method was introduced in 1978 and phased out only last year. The stories of those it affected, says Leung, made for grim reading. “I remember hearing about it when I was a lot younger and thinking: ‘Holy crap, that’s unfair,’ but it wasn’t until I started doing research for the show that I found out how horrific it was,” she says. “It is amazing it has been lifted now.”

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One Child was filmed in the UK and Hong Kong, the latter somewhere Leung has strong ties with. Her father Peter was born in the city and it is where her mother, Kar Wai Li, still lives. “I know Hong Kong well, especially where we filmed in Tai Po,” she says. “It felt nostalgic to be there. I have been going back and forth since birth. My gran has a flat there too. It is almost like home.

“During my teenage years I did enjoy partying a lot. Hong Kong was a great place to party. I enjoyed the weather and it was bustling, with so much culture. I went four times in a year which is pretty insane given it is a 16-hour flight from Scotland.”

While often pegged as a born-and-bred Motherwell girl, Leung had a more nomadic upbringing. “I was born in Dundee, lived in Ayr, then Hong Kong for around six months, followed by Hamilton and Motherwell,” she says, checking them all off on her fingers. “It was down to wherever my dad’s work took him mostly. I studied photography at the Edinburgh College of Art, then moved to Glasgow to study drama at the Royal Conservatoire of Scotland.”

Leung still calls Glasgow home, sharing a flat in the city centre with her boyfriend Eric, 26, who is a close friend of her younger brother Jonathan. Her parents divorced several years ago and her father, who owns a Chinese food wholesale firm, has since remarried. Leung has three half-siblings, Nichole, 16, Darren, 14, and Will, seven (“the baby of the family,” she says, with an affectionate smile).

She has maintained a loyal following since starring in the Harry Potter films (or “Potter” as Leung refers to the franchise). “It has been incredible because the fans I got to know and love from the beginning have been with me throughout my career,” she says. “They come to see my plays and contact me through social media. When they go to one of my shows that isn’t Potter I get really excited. They have been so supportive and I’m grateful for that.”

Not all of the “Potterhead” fanbase embraced Leung. There was a diehard contingent who, envious of her playing Radcliffe’s love interest in Harry Potter and the Order of the Phoenix, waged a vicious hate campaign which included creating an I Hate Katie website to post vitriolic and often racist comments.

I’m curious as to how Leung handled this: did she quickly need to grow a thick skin? “Looking back I can’t remember much about that part of it because I was so in denial of what was happening,” she concedes. “I put it to the back of my mind. I don’t know if that is the best way to deal with it, but that is naturally what I did in order to move on and be a good actor.

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“I was being judged purely on my looks because she [Cho Chang] is supposed to be a very beautiful girl. This all happened before the films even came out. I thought: ‘Well, I can’t do anything about the way I look, so I’m going to need to do the best acting to make up for it.’”

That can’t have been easy. Lesser mortals would have curled up into a ball and wept. “Especially at 16,” she admits, “but I look back and I’m pretty impressed with how I did handle it.”

One Child is a gritty drama and Leung appears to have thrived on tackling a meaty role. “I’ve been lucky enough to be involved in projects where I’m able to raise awareness,” she says. “It feels like I’ve played a lot of characters whose stories perhaps haven’t been told in the media, people who are a bit more invisible in society, almost like ghosts.”

She concedes that niche may prove something of double-edged sword. After playing a clutch of marginalised characters in recent years, Leung fears being typecast. “I think any actor wants to challenge themselves and to do as many different roles as possible,” she says. “In spite of what I’ve done so far being race-specific, each character has been completely different.

“I have really enjoyed everything I’ve done, but it would be great to play a character that is not down to the colour of my skin because I feel that’s the only way that people are going to watch a Chinese person on television and see I’m not an immigrant or someone who talks with a funny accent. If I could just be who I am, to play a version of myself, that would get rid of ignorance.”

It is a thread which echoes Lenny Henry’s speech at the 2014 Baftas where he spoke out about the “appalling” lack of diversity in broadcasting. This is an issue Leung feels equally strongly about. “If we are not representing what is in real life on our screens then people are going to remain ignorant, be prejudiced and maintain these stereotypes,” she says. “It could always be better and we are definitely not quite there yet.”

The recent outcry among some quarters on social media over Noma Dumezweni, an actor of South African heritage, being cast as Hermione Granger in the stage production of Harry Potter and the Cursed Child – due to open at London’s Palace Theatre in July – is a case in point.

Leung is thrilled to see Dumezweni in the role. As it transpires the pair recently had an overlapping run at the Royal Court Theatre when Leung was in You for Me for You and Dumezweni in the play Linda, having stepped in for Kim Cattrall when the Sex and the City star was forced to pull out on medical grounds only a fortnight before the show opened.

“That was the play downstairs and we were upstairs,” says Leung. “I heard so many amazing things about Noma and how incredible it was she stepped in at the last minute. I met her in the corridors a few times. I was ecstatic when I heard she was going to be playing Hermione.”

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Leung says she was buoyed to see the support Dumezweni received from JK Rowling, who quickly moved to shut down any debate, posting on Twitter: “Canon: brown eyes, frizzy hair and very clever. White skin was never specified. Rowling loves black Hermione.”

Which is exactly how it should be. Leung shudders when I mention the recent yellowface row over Scottish comedian Janette Tough, of The Krankies fame, being cast as a Japanese fashion designer in the forthcoming Absolutely Fabulous: the Movie.

“It’s wrong,” she says, her brow furrowing. “I don’t know why it is a bigger deal for people to do blackface than yellowface – they are both exactly the same thing. We’re in the 21st century and it shouldn’t be happening now.

“I don’t know why there is a comedy value to that – I don’t find it funny. It is something I would like to see disappear. I remember watching Breakfast at Tiffany’s as a child and seeing Mickey Rooney’s character [Mr Yunioshi]. It made me feel ashamed of being Chinese, seeing someone basically take the mickey out of a race.

“I would hate for other kids to see something like that on TV and feel ashamed of their own culture or who they are. I don’t think it should be happening.”

Leung talks frankly about experiencing casual racism throughout her life. “There are people who are subconsciously racist and not aware of it,” she says. “If I’m in a taxi and asked: ‘Where you off to?’ and I say: ‘I’m going to the airport’, I’ve had the driver say: ‘Oh, your English is really good …’”

She nods as my jaw hits the floor. “That kind of thing still happens,” she says. “It happened not that long ago. You get strangers coming up and saying the one Chinese or Japanese word they know, such as ‘ni hao’ or ‘konnichiwa’.

“It happens on the street or a night out in a bar. It’s sexist and racist, actually. That is something which needs to be addressed, but then again that can be solved through more diversity on our screens.”

Leung, however, has not been immune from letting the poison of such negative stereotyping seep into her own life, recounting her trepidation ahead of her first Shakespeare role playing Portia in The Merchant of Venice at the Royal Conservatoire of Scotland.

“I remember telling one of my mates at drama school that I didn’t think I would be able to do Shakespeare because I was Chinese,” she says. “I felt I wouldn’t be able to do any Shakespearean role simply because of the colour of my skin.

“But my mate was like: ‘Shut the f*** up.’ That gave me the push I needed. I realised I had been putting myself in a box when I was capable of so much more.”

For a time after the Harry Potter films, Leung was unsure about pursuing acting and considered a career in photography. “I love photography but I’m glad I’m doing acting,” she says. “It shows that if you stick with it and work hard, something will come of it – it sometimes just takes a kick up the arse from friends and family.”

Discussing her hobbies outwith work prompts Leung – a self-confessed video game geek – to break into embarrassed laughter. “Oh God, I’m so boring,” she says, with an apologetic eye roll. “I spend most of my time playing Call of Duty.

“I used to have a head set when I played against my brother and his friends [online] but now one of his friends [Eric] is my boyfriend, so we live together and we play video games together – we don’t need the headsets any more.”

She paints a blissful picture of coupled-up life. “We watch a lot of Netflix and Amazon Prime, drink red wine and eat cheese in our pyjamas. There’s lots of chocolate involved,” says Leung. “We want a dog, but we’re waiting until we find a lovely place with a nice park nearby.”

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As for what Katie does next? Having talked animatedly about her love of stage acting and a role in an upcoming (as yet unnamed) film project, Leung’s face clouds when asked if there is anything she would rule out. “More and more when I see a script that requires a Chinese accent of any kind, I flinch a little bit,” she says. “Obviously I can’t just say no for that reason, but I’m flinching.”

Leung exudes steely resilience and sunny optimism – a seemingly incompatible yet apparently winning combination. “Perseverance is important. Rejection is the biggest thing I’ve had to overcome, but that happens to all actors,” she says. “It doesn’t get easier but you learn to appreciate all the rejections – and the jobs when they come. I’m learning to embrace everything that comes my way.”

One Child begins on BBC Two this Wednesday at 9pm. Thanks to Hotel du Vin at One Devonshire Gardens, Glasgow (hotelduvin.com)