We don't yet have a reliable history for this period; there is no sign on the continent of migration to Britain; though we may surmise the points from which some set sail, we can't be sure that those points were their homeland. Examination of apparently settler inhumations in Britain has not told us where on the continent they may have come from. The fortifications of the Saxon Shore are pre-Saxon settlement by at least a century. The ship of Sutton Hoo looks to have come from southern Sweden. I wouldn't trust anything written in the name of Gildas.
I think we have a long way to go on this.