Comment by vidarh

Depends. Usually black if you don't know any more. Black British if you know they are British, but a lot of black people here are born in Africa or the Caribbean, and not all will be pleased to be described as British (some will take active offense, given Britains colonial past) and will prefer you to use their country or African/Caribbean depending on context.

My ex would probably grudgingly accept black British, but would describe herself as black, Nigerian, or African, despite also having British citizenship.

If you're considering how to describe someone who is present, then presumably you have a good reason and can explain the reason and ask what they prefer. If you're describing someone by appearance, 'black' is the safest most places in the UK unless you already know what they prefer.

"Nobody" uses "African British".