In USA, while the term "black" is not offensive, the politically correct term for blacks is "African Americans." What is the politically correct term in Britain? African British? Is there a term to refer to black people living anywhere in the UK? Also, what is your politically correct term for people of Asian, Hispanic, Middle Eastern, or Native American descent? What if the person was white, but was born and raised in Africa, and then immigrated to Wales?
In my personal opinion, the correct way to label would be "Kenyan American," "Italian German," "Vietnamese Scottish," "English Japanese," "Polish Russian," "Papua New Guinean Mexican," etc. But clearly that's not the way it's officially done.