The singer told Company that everything changed for her when she hooked up with the Fall to Grace star.
"I didn't think it was realistic to follow my dreams when I was younger," said La Havas - who also spoke of her love for Jill Scott, Mary J Blige and Lauryn Hill.
"I thought I'd end up an art teacher, so I went to art college. Soon after, I was introduced by friends to Paloma. She invited me on the road as a backing singer with her for 18 months."
"I got to see her rise and she taught me to always look fabulous. Once she wore six-inch stripper platforms to a muddy festival - totally my inspiration."
She added: "I wrote my first song at 11… All [my] songs are very personal and about love.
"I had this moment the other day when I was playing 'Age', the song about being with an older man, to my current boyfriend's parents - and I got all nervous about what they were going to think!"
Of Prince getting in touch about her music, La Havas said: "When I was told Prince was going to call, I assumed it was a hoax.
"Obviously, I forgot my phone and was in a pub in Hackney. But he called my boyfriend's phone instead and it was so noisy that I had to find a nearby alleyway."
She continued: "There I was, in Clapton, in a dodgy alley, on the phone to Prince! He was so complimentary.
"Then Stevie Wonder came to a gig in LA last summer… After the show, we chilled and drank some wine, he played me his new song. It was so beautiful, it made me cry."
The full interview appears in the March issue of Company, on sale now. See behind-the-scenes action from the shoot on the Company website.
Photo gallery - Mercury Music Prize 2012 ceremony:
Copyright: PA Images Yui Mok/PA Wire