The Vikings had to fight for their new lands and the Scottish clans and the English Saxons resisted strongly.
Eventually, north eastern England became Viking land the Danelaw, although, as the centuries passed, Saxon English and Viking Danes became intermixed.
Viking times in England ended when English King Harold beat a Norwegian invasion in 1066 only to be beaten in turn by William the Conqueror, although he was actually of Viking descent, too!