Lots of ways:
siphons off malcontents like the Puritans
provides new foods, like potato, which change nutrition throughout Europe
new economic circles, e.g. triangle trade
huge infusion of gold & silver through Spain, changing balance of power
The isle of Britannia has been invaded time after time. The Celts, the Angles, the Saxons, the Normans all took over the whole place at different times. The Danes, Romans, Picts spiced things up in between.
Anglo-Saxon is a designation after the fact. In 1066, the Normans invaded and defeated...