"Transatlantic" is a stylized pseudo-British/American that many actors and performers trained in, less common now.

   Pop music is theatrical, and a song is theatrical in the basic sense of mixing arts. I don't mind a singer singing in the accent of a barnyard animal if it sounds good. It's a non-issue to me. Just bcause you learned an accent where you grew up doesn't make it real or natural, just handy--it just disposes you to be convincing with it, and you don't need to explain why you use it, to most people.