OP is right. Black Brits refer to themselves as British though rather than African-Brit (or similar). Black Brit is used at a push when the distinction actually makes a difference (like as part of a political point) BUT almost never (ever) as African-Brit unless they (or their family) have recently arrived from Africa.
Why would we refer to ourselves as 'African-British' when we can identify the African/Caribbean countries we come from? If you don't see a black person over here referring to themselves by their country of origin then you'd likely see them referring to themselves as 'black british'. Btw, almost all black people over here have recently arrived- the first wave of black immigration came in the 1950s, and that was mostly Afro-Caribbean people.
50% of black males (or thereabouts) are in a mixed relationship so the level of mixing is high. There is and was little to no slavery in the UK and no KKK/Civil Rights/Sundown towns/segregation/etc etc etc. So the surface animosity is NOT at the level that you have in the states. Even now there is less segregation and in the big cities almost no one takes notice of mixed friends or couples. The US norm where you lead with cultural / racial affiliation first and person next is almost absent from UK public life.
I wonder why so many black people trust in these statistics cultivated by white people for a specific purpose without ever questioning the motive of it? 50% of black men here are not in a mixed relationship- how could someone even believe that?
Under those circumstances where socially many people are fine with each other many blacks do not subscribe to the notion that 'Whites are evil". The system stymies blacks economically but as economical achievement is not the be-all and end-all of life as it is in the states many people will not even notice this. As this economy changes this is becoming more noticeable but it is still far from widespread.
Many people are not fine with each other. Many black people know that once they step out of London, and even some places within the city, that they are not welcome. White people have a way of making you feel like that without even uttering a word. Yes, racism is generally more subtle here than it is in America but you've got to consider the fact that blacks over here don't even take up 3% of the population. We all know that once that number starts to rise, these white people will start brandishing their racism with much more force. Also, you don't think that black people over here don't know that white people economically oppress us systematically?
In short "White Supremacy" is not a belief that has gained more than negligible traction in the UK and to be fair, the more logical mind of the Brit would find it hard to use a term which embodies the very notion that it is supposed to be fighting. "White Ideology" maybe, "White Paranoia" perhaps, 'White
Supremacy" NEVER.
If you ask the average black person in England/the UK "what" they are they will say "British". End of story.
No, they would say likely say that they're British, followed by their country of origin or their country of origin, followed by "British". This is especially true for those of direct African descent, who actually make up the majority of black brits now. If you, as an American, ask them what they are then they're likely to say "British" though, as you'd already know that they are black. Just like an American black would tell me that they are American if I asked them what they were.
Also, not pinpointing white supremacy exactly as that doesn't mean that they don't believe that it exists. To them, it might just be boiled down to 'racism', which many black people, not just UK blacks mistake it as.