One of the Norman Kings (Henry II?) differentiated penalties for his English and Welsh subjects, implying separate communities in England into early medieval times. This is before the conquest of Wales, as such. So that particular integration certainly took some time. (Source Morris: The Age of Arthur)   

It would seem logical that the take-over by one culture of another would sometimes be violent and sometimes reasonably "civilised", and likely both side-by-side depending upon local circumstances and characters, and of course time. The Anglo-Saxon conquest of England shows features of both - I don't know, but doubt, that the evidence is in for the Iceni/Parisi/Belgae and other late "Celtic" invasions, let alone further back. As much of the evidence seems to rely on ritual such as funeral customs, a change of religion would be as likely an explanation as a movement of peoples.

First rule of archaeology: if you don't understand it, call it ritual.