People in England during the Viking period were indeed aware of the Angle and Saxon invasions. The Anglo-Saxon Chronicle of the 9th century was written during the rule of Alfred the Great, who famously defended his realm against Viking conquest. The Anglo-Saxon Chronicle tells the history of Britain up to that point as it was known to the Anglo-Saxons, including the invasions of Caesar, a slightly misdated history of Roman Judaea, an overview of important dates in the history of the Roman Empire, the wars between the Romano-Britons and the Angles, and many other events in the following centuries.

For example, here is an excerpt:

A.D. 449. This year Marcian and Valentinian assumed the empire, and reigned seven winters. In their days Hengest and Horsa, invited by Wurtgern, king of the Britons to his assistance, landed in Britain in a place that is called Ipwinesfleet; first of all to support the Britons, but they afterwards fought against them. The king directed them to fight against the Picts; and they did so; and obtained the victory wheresoever they came. They then sent to the Angles, and desired them to send more assistance. They described the worthlessness of the Britons, and the richness of the land. They then sent them greater support. Then came the men from three powers of Germany; the Old Saxons, the Angles, and the Jutes. From the Jutes are descended the men of Kent, the Wightwarians (that is, the tribe that now dwelleth in the Isle of Wight), and that kindred in Wessex that men yet call the kindred of the Jutes. From the Old Saxons came the people of Essex and Sussex and Wessex. From Anglia, which has ever since remained waste between the Jutes and the Saxons, came the East Angles, the Middle Angles, the Mercians, and all of those north of the Humber. Their leaders were two brothers, Hengest and Horsa; who were the sons of Wihtgils; Wihtgils was the son of Witta, Witta of Wecta, Wecta of Woden. From this Woden arose all our royal kindred, and that of the Southumbrians also.

So the English were definitely aware of their connection with continental tribes.

Here's a link: [12th century version of the Anglo Saxon Chronicle] (http://avalon.law.yale.edu/subject_menus/angsax.asp)