The first memory is of a picture, a picture of a beautiful face, dark eyes, exotic lips, glamorous, serene.

To a nine-year-old child, it looks mysterious, strange; the face of a woman from a long time ago.

The second memory is of a letter, a bitter little thing written by a teacher in the 1980s. It says: your dreams will never come true. How can anyone say something like that to a child?

Finally, the third memory: a phone call, a tearful call from the Red Road Flats in Glasgow back home to Arbroath. Karen Cargill remembers what she said during that call: “I want to come home dad. Please let me come home.”

More than 20 years on from all those events, Karen Cargill is sitting in a cafe in Glasgow and thinking herself back through them, working her way along the string of memories, trying to figure out how she got here, how she became what she is now: Scotland’s newest global opera star.

That first memory – the one of the beautiful face – comes back to Cargill when I ask her how she discovered opera. Immediately, she goes back to Arbroath and heads down to a house near the seafront where her singing teacher lived. In one of the rooms is a pile of LPs and on top of them is a 1950s box-set and there, on the front of the box, is the picture of the face.

When Cargill first saw that image, all she knew was that it was a woman who looked astonishing, theatrical, and then her teacher told her the woman’s name: Maria Callas. “I’ve had a love affair with Callas ever since,” says Cargill.

Over double espressos in the cafe near Cargill’s home, we talk about Callas and there are some interesting contrasts at work. Callas was famously brittle, lonely, the diva, but Cargill, 35, is known for being the opposite: friendly, unpretentious, the anti-diva and – despite the fact she now has an impressive international reputation and is in demand at the very top – it’s true: she is.

“I don’t know where the anti-diva thing came from,” she says. “Maybe it’s because I haven’t changed – and anyway, it doesn’t happen very often that you go into a rehearsal room and see divas. I’ve seen one or two but you can forgive people certain behaviour because what we do is extraordinary and people pay to come and hear you and expect a certain standard. It means that every time is frightening.”

There is something in the life of the diva though – and in the life of Callas in particular – that Cargill does recognise. She may be married and have a young son, but she can still recognise the loneliness of Callas. “You can imagine her sort of life,” she says, “a very lonely life and it is lonely, my life, when I’m travelling.” And then, because Cargill’s default setting is positive, she explains how she copes: there’s Skype for starters and anyway, she adds with a laugh, it’s nice sometimes to get the chance to eat room service in bed without having a toddler running around you.

We talk about her toddler, Adam, for a bit. He’s two-and-a-half and likes to sing around the house – Lady Gaga mainly. Cargill says that’s what she was like when she was growing up, except that it was Boney M and a bit of Abba. Cargill’s parents – her dad was a plumber, her mum worked in a bank – never pushed her into music like some parents do – if anything, what they did was allow Cargill to push herself into it.

It was a different story with Cargill’s teachers though, and that’s where the second memory comes in, the memory of that letter from the head of music at Carnoustie Academy.

“About half-way through my first year, my parents got a letter home from the head of music saying I wasn’t going to make anything of a music career and that I should probably focus my energies elsewhere.” Cargill’s face tightens as she thinks about it. “I’d love to go back and say to that guy, ‘It’s because I knew somewhere in me, I don’t know where, that I could do this, and that I loved it and that I wanted to do it that it’s happened’.”

And here’s how it happened: without much, if any, support from her teachers, Cargill slogged away and won a place at the Royal Scottish Academy of Music and Drama in Glasgow where she learned about opera, and learned that she loved it. It was hard though, particularly the first day.

“Here’s me, from this tiny wee place, and I’m in Glasgow living in the Red Road flats,” says Cargill. “It was a complete culture shock and I got my timetable and phoned my mum and dad in floods of tears and said: ‘I need to come home.’ But my dad said, ‘It’s your first day, you’re all right, don’t panic’.”

So Cargill followed that advice and did her first day, and slowly things started to be OK, although she can’t remember exactly when they turned around. Basically, she stuck at it and that’s what she’s like: she’s got tenacity but equally she says she doesn’t want to be too tenacious, and that’s where the modesty kicks in. There are a lot of these contrasting qualities in Cargill and it’s probably because she’s an opera star and we expect opera stars to be a certain way, and she isn’t. The contrast is even in the way she sounds: on stage, the mezzo-soprano voice is astonishing and big and dominating; in a cafe having a chat, the voice is warm and soft and full of lots of couthy, Arbroathian consonants.

It’s obvious Cargill is fond of Arbroath, where her parents still live, but the moment she realised she wanted to be an opera singer actually happened 3000 miles away. When she was 22, Cargill was offered an exchange to Toronto University and it was there she realised opera was what she wanted to do.

“When I was a teenager, opera seemed like a million miles away,” she says. “It seemed like something I possibly could do but my voice wasn’t mature enough. I wasn’t mature enough. I also think I’d been at the RSAMD for too long. It wasn’t always a positive experience for me. I felt there was an awful lot of criticism for a long time. And that really did bear down on me quite heavily. Really, I’d had enough. My confidence had taken a knock and then I went to Toronto and people said, ‘Oh, you are good at what you do’.”

Returning from Canada and graduating from the academy, Cargill’s career built steadily before accelerating rapidly in the last three years or so. When I ask her how it’s been recently, she laughs and mimes a plane taking off and she’s right: she’s now performed with some of the greatest orchestras and conductors, including the Berlin Philharmonic under Simon Rattle; she’s a favourite of Donald Runnicles, chief conductor of the BBC Scottish Symphony Orchestra; and next year she will make her debut at the Royal Opera House and at The Met in New York.

There’s also been work with Scottish Opera, of course, most memorably in 2009 when she sang the title role in Rossini’s The Italian Girl in Algiers in a production that had a curious twist: it was set during the making of a soap opera. Cargill says she approves of this kind of mixing of styles because that’s how she is herself: a mix of modern and traditional, high and low, Radio 3 and Radio 1.

Cargill also tells me that professionally, she seems to have found a niche that works for her. She can work all over the world by jumping on a plane and she’s made her career fit around her son by doing a little more concert work than opera of late.

What she hasn’t done so much of, and would like to, is studio recordings but even as she talks about this, the modesty kicks in again. “I’d have to listen to myself,” she says, “and I’m not sure about that.” Doesn’t success wipe out that kind of self-doubt, I ask; doesn’t experience win over the fear that you might not be good enough? Not really, she says: “The fear only gets worse because the expectation is higher.”

And there it is again: the star who is loved and praised but who is also modest and self-analysing. It’s an engaging combination, a new way of being a diva, Karen Cargill’s way.

Karen Cargill sings Mahler and Brahms with the BBC SSO at City Halls, Glasgow, on Thursday, Perth Concert Hall on April 8 and the Usher Hall, Edinburgh, on April 10.

Karen Cargill, opera singer