The Saxons, Angles and Jutes that invaded after the fall of Rome all generally came from Denmark[1].

Most of the Norse who subsequently invaded in the 700-1000 were either Danes or Norwegians[2], and settled in pretty large numbers in East Anglia, Northumbria and Mercia.

Then the Normans, who were in large part Danes and Norwegians that had gotten bought off with a piece of France came over in 1066.

I don't know how accurate this is, but in Bernard Cornwell's Uhtred series, English and Danish are different enough that they aren't really mutually intelligible.

[1] https://en.wikipedia.org/wiki/Angles#/media/File:Angles_saxo...

[2] https://en.wikipedia.org/wiki/Great_Heathen_Army

Probably a bit of both. 'Old English' is probably closer to Viking-era Danish than, say, modern German and of course the Vikings also did conquer parts of England.

Vikings and also the Norse who had settled in Normandy and had adopted lots of old French vocab but retained some ancestral vocabulary when they invaded and subjugated the by then indigenous Anglo-Saxons.

Also north east England was under Danish influence for quite a while.

I can't remember where, but I read there is a theory that English originated as a creole of Anglo-Saxon and Old Norse. The two languages had similar vocabulary (e.g. AS scirt -- modern English shirt -- vs ON skirt, both originally referring to a unisex knee-length tunic), but different inflections: the vocabulary was kept but much of the inflection was dropped, which is why English is morphologically so much simpler than, say, German.

looks like a good oppertunity to plug one of my favorite podcasts, The History of English Podcast http://historyofenglishpodcast.com/, if you're curious about history of the language and its indo-european cousins its fascinating.

I think it is because of the latter. The Anglo-Saxons, while coming from an area that coincides with modern day Denmark, did not speak (an ancient form of) Danish.