It's almost impossible to sing certain songs correctly with a British accent. The rhythm, the cadence, the timing, etc. would all be off. Even if the singer isn't consciously trying to sound "American" or "black" or whatever, it will likely come out that way in order to sing the song right. That said, there are regional accents in music, like a white Southern or twangy accent in country music, or black Southern in blues and soul and R&B, or Jamaican/Caribbean in reggae and related forms of music. That's why Australian country singer Keith Urban has a thick Aussie accent when he speaks, but sounds like he's from Tennessee when he sings, or why British neo-soul singer Amy Winehouse sounded like a black woman when she sang (many people noted similarities with black American singer Lauryn Hill), but like a typical white British woman from the south of England when she spoke. And like others have said, a "neutral" accent in singing will sound more "American" than anything else.