“The other significant 5th-century event in Britain was the arrival of the Anglo-Saxons.”
That was a critical point in Britain’s history, and left a much deeper impression on the island (most specifically the English language itself - spoken much more widely than Italian). Immediately prior to the Norman invasion, the Saxon king Harold had just defeated a Viking invasion and had to double-time to meet the Normans; accounts of the battle of Hastings, in which Harold was killed, indicate a battle the Normans very nearly lost. The Saxons snatched defeat from the jaws of victory by breaking their shield wall (which had held for the duration of the battle) and charging. A special Norman unit was then able to kill Harold, and rather than be driven back to Normandy for lack of supplies the Norman forces were able to win the day.
These were hardly barbarian invasions; William was familiar with Harold and thought he was the rightful heir to Harold’s throne (they had made some agreement years earlier).