The 28-year-old credits a big part of that success and finding her best voice to her work with those producers and co-writers.
"I think finding my confidence just came through writing with the right people. It's been really important to me to feel comfortable in a studio, because I felt so inexperienced - and that's why on the album I worked with only three main people, because those were the people that I trusted and found confidence with.
"And they made me feel comfortable about expressing myself and comfortable that I could get things wrong.
"So I think it's really down to them, drawing me out of myself, especially Dave Okumu."
Of course, her process with each of them was quite different and allowed her explore various songwriting approaches.
"Dave is ridiculously generous. Like with Devotion, after talking about all the things that I love, he came in and went, 'I've kind of made this thing for you', which was amazing, and then I started adding the verses to it.
"With Julio Bashmore it will start with a beat, and I'll sing over it, more like what I did with SBTRKT and Joker, vocalising something over the top and writing to that.
"And with Kid Harpoon, we'd just go for very long lunches and talk about everything, and whatever we talked about the most, we'd go and write a song about."
In fact, that's how one of her biggest singles came about - Wildest Moments was born out of a conversation the pair had at her manager's wedding.
"My best friend had been a real prat to me and she'd thrown a cake in my face. So he was asking me, 'What happened with Sarah? That was pretty weird!'
"And we were talking, and I was saying, you know, 'I'm really sick of us fighting with each other all the time, but we seem to be either really amazing or really terrible' and it would swing backwards and forwards."
Ware's distinctive, tasteful style - a blue note-tinged mix of electro, dance, soul, pop, and 80s grooves reminiscent of Prince, Grace Jones and Whitney Houston - seems to be a product of her background, a mix of her love for the R&B her mother used to play, and teenage years spent dancing to drum 'n' bass.
"My family are quite an influence - not artistically I don't think, but motivationally they really help. My siblings aren't really musical [she has a brother and sister], but I was a big R&B fan when I was young, and I think that came from my mum being obsessed with it, and my kind of absorbing it all."
She was also a fan of her mum's Frank Sinatra and Ella Fitzgerald tapes - enough to leave her with a bit of a yearning to perform them for an audience one day.
"I just love singing jazz standards. I don't think I'm the best at it at all, I don't think I'm very good, but it's just the way that I learned how to use my voice, I think.
"I would love to do some sort of one-off concert and just sing loads of Gershwin and Cole Porter," she laughs.
Perhaps surprisingly then, it was the time spent dancing nights away to drum 'n' bass with her young friends that eventually led her to see a potential opportunity to pursue singing.
"I was never going to make drum 'n' bass, but I think I always loved the idea of female vocalists on a dance track - they were always my favourite songs in the club.
"I always liked the idea of singing along to a beat and I guess I used to think it was a good option, because it meant there was less attention on me - lending your vocals to a dance track would still leave the focus on the DJ."
Of course, the attention is now firmly on her, and it's a state that Ware has slowly adjusted to, delighted that the attention so far has been resoundingly positive.
"It still feels pretty strange, pretty unbelievable, but it's a huge compliment and it's a lot of fun, I guess. And I can't believe people have been so kind about me, they're very generous. I definitely feel better about [the attention] now. I've got an album out, so hopefully that means my songwriting has improved.
"And I just want to keep doing it now, keep writing, and keep performing."
Who: Rising British star Jessie Ware and her three-piece band
When and where: 7.05pm, Cactus Cat Stage
Listen to: Devotion (2012)
- TimeOut