By the time black people were settling in Britain in significant numbers- during and after WWII- the folk tradition had become moribund. There were small older black communities, notably in seaports such as London, Cardiff and Liverpool, but they perhaps shared the musical culture with the rest of the community. In any case the urban traditions were being subsumed into music hall and other commercial entertainment from the mid 19th century onwards.

Unlike the Americas, we didn't import slaves in large numbers- we sold them to the plantations of the West Indies and the American colonies. And the culture of the few in the UK would have been seen at best as 'exotic'- few enough people recorded any working-class traditions at all, and those that did would not bother with music that didn't accord with their ideas of quaint, ancient, patriotic or whatever their particular agenda was.

Having said which, the best player of harmonica for Irish music I've ever known was Asian- anyone know what Sharad (if I've remembered his name right) is doing? He used to play in Birmingham in the 70s.