There's been some very interesting research over the last few years - based on DNA block studies, which indicates that - contrary to conventional historical accounts, the Celtic tribes were not spread throughout what we now call England and, consequently, were not "driven out" by the Romans or anyone else into the strongholds of Wales, etc. Celtic entry seems to have come into Britain through the South-West from Spain. The greater part of England was already populated by people of different stock who had very strong genetic links to peoples in Friesland and other Germanic tribes. The passing of the Romans opened up the routes for more interchange between existing tribal groups.

Bede and other chroniclers - who had agendas of their own - should be taken with a pinch of salt.