Even without the Norman invasion, the British Royal family would be descendent from Norsemen through Godwinson's mother, daughter of Sweyn Forkbeard, grandchild of Harold Bluetooth (King of Denmark/Norway and inventor of frustrating wireless protocols).
After 1066, England was pretty awful for the Anglo-Saxon warriors/noblemen, a good number of them also fecked off to Byzantium and joined the Varangian guard like Vikings before them. They also created settlements in what is now Ukraine.