Well its little unclear in a lot of cases. Scholars aren't even sure how violent the "conquest" of Britain was in the first place for example.

Peter Heather argues that the traditional narrative of invasion and conquest in Britain is more or less accurate in big picture, and that this process resulted in the fragmentation and splitting of local powers as migrant warlords divvied up the spoils among their followers. Each warlord would distribute the spoils of conquest, land, slaves, loot, and so on, between his followers and that this ad hoc basis of wealth re-distribution eventually gave rise to the later kingdoms of England.

Robin Fleming however argues that there is no compelling contemporary evidence to assume such a violent seizure of wealth and land. Instead she posits that migration was more or less peaceful into Britain and only over the course of several decades did new polities emerge that legitimized their newfound rule and power with appeals to a largely mythologized period of history that involved violence and conquest.

However in both cases, the key is that the incoming groups were relatively small scale by the standards of late Antiquity. Britain was not subjected to the large movement of armies over its territory like Italy, Illyria, and Gaul were. The numbers of people moving into Britain were likely still significant, but they did not constitute a united group of people or an invading army.

The situation on the continent was a little different. Gaul was taken over by the Franks, eventually, following a succession of other powers such as the Visigoths and various Roman successors being edged out over time. But the Roman population of Gaul did not disappear as it did in much of Britain, and Romans remained in positions of power, especially in southern Gaul for quite a long period of time. Long enough for differences in legal norms and protections to become enshrined into law.

However in Northern Gaul, the situation was different. Here, as in Britian, there had been a near total economic collapse in the early 5th century resulting in devastation to urban life in Gaul. Unlike in England however the newcomers were invested in maintaining the appearance of Roman continuity and so the break with Roman civilization was not as neat as it was in Britain.