Why did Rome lose Britain to the Germanic Anglo-Saxons?
The Romans no longer had any military presence in Britain because its legions had been withdrawn to the Continent in 407 in order to defend Italy and Rome itself from the Goths (who sacked Rome anyway in 410). What could subsequent Roman central governments do? They had trouble enough defending their own new capital Ravenna, and had lost control over all Northern provinces. Winning back control over Gaul was far more pressing than worrying about remote Britain; besides, they couldn’t stop those Saxon boat people anyway. The Scots seemed more likely to conquer Britain than a limited number of Saxons would be, so for the Romans it probably seemed the lesser evil to endorse these latter. And with an eye on retaking the province at a later date, it was better to have several warring factions there than to have it firmly in the hands of one single strong enemy. Of course that policy didn’t work out the way the Romans had intended.