By black British I mean people living in Britain prior to enlisting or being conscripted (regardless of what ultimate regiment they served in), OR black soldiers serving in the British "metropolitan" army regardless of country of origin.
thought this was a bit of an interesting point as there is plenty of literature on BWIR and also the KAR but practically nothing, as far as I can tell, on black troops originating or serving in a British (geographic) regiment.
The word you are looking for is 'domiciled black British'.
The answer is unfortunately that we don't fully know. A big obstacle for any researcher dealing with minorities in Europe (unlike the United States) is that the topic of race is not commonly mentioned on the rosters, draft cards, or other military documents that attests to an individual's service. Many, if not all, domiciled black British soldiers did not have any names that would make them stick out of a crowd when you're going through lists looking for them. You could sometimes be in luck if you manage to find a medical note commenting on the soldier's race, usually in a negative form, but this isn't a frequent occurrence. Many researchers today investigating black British soldiers in the First and Second World War have to base their research on material like local and family history, contemporary and post-war reports of black British servicemen in newspapers and other popular media as well as the occasional mentions in official government and military documentation.
This particular area remains very understudied and it's only recently that historians have begun writing on the topic of black British soldiers in the First World War, such as Ray Costello's Black Tommies: British Soldiers of African Descent in the First World War (2015) or Stephen Bourne's Black Poppies: Britain's Black Community and the Great War (which was given a revised edition in 2019). This also makes it very difficult right now to make a proper judgement on just how many black British soldiers there were during the First World War in regular British regiments. What is certain is that new faces and new life stories pop up all the time, giving researchers new names to add to an ever-growing list. Sometimes, if we're lucky, we're even given an entire diary, such as in the case of Arthur Roberts who participated in the Battle of Passchendaele and whose wartime diary was published in 2014 as As Good as Any Man: Scotland's Black Tommy.
I put defined in comments, but I meant description