It took a while for Calvi to realise she wanted to be a singer, though.
Returning to her parents' home after university, Calvi played guitar with some bands to gain some experience before deciding that she couldn't ignore her dream and embarked on the hefty task of teaching herself to sing.
"I didn't tell anyone at first," she recalls. "I used to wait until everyone had left the house and then I closed all the curtains and went into a room where I thought no one could hear me and I practised scales, building up my range, my breath control.
"Then I'd listen to singers I loved like Nina Simone and Edith Piaf and think about what it was that they were doing that was really moving me and touching me and seeing if I could find it in my own voice.
"I really knew that I wanted a rich, powerful, deep voice, which is very different from my speaking voice, so I had to almost chip away to find it because it's such an emotional thing being a singer. A lot of it was letting go of the fear of being really open and vulnerable. When you sing really loudly and with a really rich deep voice, you give everything of yourself."
She didn't tell anyone about her big plans because she thought people would doubt her and not think her capable of doing something so public, particularly considering how quiet and reserved she could be. And she really is.
Sat in a meeting room in her record company, she seems completely fragile, barely moving and speaking in a whisper: "I knew people would be like: 'What? Why is she trying to be a singer? She's so not the sort of person who would be a singer.' But here I am."
You would never suspect that this unassuming woman could be responsible for such an enormously powerful voice, which lends the album drama and intensity. In fact, the entire record commands your attention, and is far removed from what makes up the majority of the charts today.
It is challenging and diverse, drawing on influences that span continents and centuries, and tackles themes such as passion, lust and loneliness.
"I didn't want to write music thinking, 'Oh I have to try and make people like this'. I just wanted to please myself and make the music really honest, feel creatively happy and not worry about whether it was commercial or fashionable in any way."
But fashionable it is, and Calvi has found herself the toast of parties thrown by the likes of Chanel and Gucci, as well as being embraced by publications such as Vogue, who have latched on to her seductive red-and-black stage aesthetic.
"When I was thinking about how to represent the music visually, it was really important, because I feel like every aspect is part of the art and I want to be involved in every bit of it," she explains. "I took inspiration from flamenco outfits because I really like the way they express the drama and passion of their music; I try to be like a male flamenco dancer.
"It's strong but it's very dramatic, and I think it kind of represents this sense of fearlessness that I feel when I'm playing music. You want to create a moment with an audience and you want it to feel special, so I like dressing up for it. It's nice."
All the interest in her from the fashion world baffles her, though. She is unsure why they've taken such a shine to her. "I guess it's just because my vision is really strong and that I think about all elements of it, so I guess that's appealing for people who are visually inclined," she shrugs.
Calvi's live performances are an eerie and entrancing visual treat, which is not surprising considering her history in art, as well as her love of film directors who use vibrant cinematography to contribute to the plot, such as David Lynch and Wong Kar-wai.
However, she waves away the suggestion that the Anna Calvi on stage is a work of art that she has created.
"It's not a character but it's a different side of me. Performing brings out the more passionate side of me, the side of me that's strong and more powerful, I suppose." Considering that the music is so different to much of what is played on the radio these days, has it surprised Calvi that her music has been embraced so fervently?
"I did the best piece of work I could possibly do at that time of my life and I felt happy with it, so that's all you can really hope for. If people like it, then that's an added bonus and that's really great. I guess it is surprising in a way because I really thought that I could be the only one who really wants to hear this."
She's so collected, focused and serious, that I have to ask if she ever, you know, slobs around in her pyjamas watching bad American sitcoms.
"Yeah of course!" she cries, laughing for the first time. "Look, people who don't know you will have a very two-dimensional view of who you are but that's OK, it's normal. I don't really want people to know who I am, that's for my friends and my family to know.
"I want people to know my music and my art which I try and express as fully and as richly as I can but, yeah, everyone has stuff that maybe you're a bit embarrassed about and wouldn't necessarily want to mention in an interview."
And so for the first time, the professional mask falls and she reveals a small glimmer of the other Anna Calvi, before she carefully composes herself again, and the icy cool returns.
-The Independent
