Well said, Will Fly.

I wonder how many people posting here actually sing. I sing a lot. And I'm here to tell you that when you sing a lot, when your voice gets strong and practiced, that your brain can decide that it's time to sing a certain song, but your voice then takes over and decides what accent and timbre to sing that song in.

If you are British, then by age 30 or 60 you have heard at least a decade's worth of American, and your brain and your voice have an American accent stored in your system. It's your own.

With the blues it is relevant that the American southern accent (not that there is only one American southern accent) is descended from English working-class accents.