From what I can gather about Britain in the 5th century, around the time that the last regular Roman troops (and provincial officials loyal to Rome rather than the province itself) left Britain, the Picts started raiding the province.
After a while, a Briton king named Vortigern invited Saxons to settle in Brtain in return for their help against the Picts. That kind of backfired when the Saxons revolted against him (this revolt is said to have included the original "Night of Long Knives"); soon enough a considerable part of modern-day England was occupied by Saxons, Angles and Jutes.
So, assuming that this is correct at in general terms -what would have happened, had the Saxons NOT been invited to Britain?
By this time, presumably the Saxon had already been raiding Britain or would at the very least have started soon. Could Post-Roman Britain had held out against both Pictish and Saxon (and Angle and Jute) raiders, and presumably Irish raiders as well? Could they have prevented the Saxon migration to Britain, or limited and/or slowed it down?
Could a recognizably Roman successor state Britain - or a collection of Roman and/or Celtic Briton nations (analogous to the various Anglo-Saxon kingdoms later on) - have survived until at least the beginning of the Viking Age? Or was Britain turning Anglo-Saxon to more or less the historical extent pretty much unavoidable?