There definitely is such thing as a British accent. I teach English from textbooks that have examples with American, British, and Australian accents.
My students prefer the American accent because it's the easiest to understand. I suspect it's really because Americans use smaller words.
Of course, after the "British invasion" (and more recently, a slew of insanely popular artists from England such as Coldplay, Radiohead, Keane, Muse, Sting, etc.) a huge number of American artists began employing British pronunciations in their singing, particularly when it comes to vowels and R's.
So, if she sounds "British" it could be because she spent time in England, but it could just as well be because she listens to American music.