Perhaps not to the casual American ear, but there actually is an audible difference. It's slight, but it's there.
There is also a sort of hybrid British/Caribbean accent that some English blacks purposely accentuate when speaking. It's a cultural thing, which many of them can turn off at will.
Read Thomas Sowell’s “White Liberals, Black Rednecks”.
A lot of the language and poor grammar we associate with inner city blacks is very similar to poor Southern white lingo ... because that’s where most blacks came from four to five generations ago.
We mock whites who still speak that way, but for blacks, it is raised to an honorable dialect.