Hugh "Lupus" d'Avranches, 1st Earl of Chester - Heraldic hints on Hugh

I don't think the arms will help us here. If this is the 1580 Visitation then we're talking about a period some 500 years after events. As far as heraldry itself, we know from the Bayeux Tapestry that there were no hereditary arms at the time of the Conquest, and probably not in the generation after. The earliest documented coat of arms is often said to be on the tomb of Geoffrey of Anjou (died 1151). It seems to be the generation after him when sons first began inheriting their father's shield emblems.

Probably the arms of England impaling Chester are from a time when the heir to the English throne was also Earl of Chester (after 1265).