The Roman territory in Britain had always been subject to raids by tribes from Ireland, Scotland and northern Europe. After the Roman legions withdrew the raids increased. This led the local British chieftains to solicit help from mercenary warriors based on the continent. During the period from around 410AD to 850AD migrants following these first warrior bands moved into Britain and began to displace the indigenous Britons, forcing them west into what is now Wales and Cornwall.
This was not an invasion as such and it was as much a cultural change as a population change, the locals adopting the rural lifestyle of the new immigrants, moving away from the Roman towns and cities.