The fact that the Angles and Saxons were from an area that is currently Denmark means nothing. Territories, country borders and the languages and cultures occupying them have changed significantly in the north of Europe after the collapse of the roman empire to the present day.
The angles and saxons spoke a western germanic language, whereas modern danish is a northern germanic language.
EDIT: as a side node: Frisian is the language commonly regarded as being closest to English
Look at my lists of Norwegian translations. Most either apply directly for Danish too, or with minor changes ("Bokmål", the written language used by a majority of Norwegians, was largely derived from Danish, and hasn't diverged all that much)
I'm pretty sure there are, at least I think I see Norwegians all the time : )
When you know Norwegian or Danish you can see a lot of similarities. The explanation I got was that around year 1000 Norway/Denmark was pretty much a naval superpower.
It's actually more recent. From the mid 1300's the Norwegian and Danish monarchy merged through marriage, and Denmark became by far the dominant party in the union. (Schelswig-Holsten was also for some time part of
The union lasted until 1814, when Denmark (and by extension Norway) had supported Napoleon, and Sweden had joined the other side. Sweden got Norway as a "price". But during that period, a lot of people had started preparing for an attempt at Norwegian independence. And while we entered into a looser union with Sweden, there was a long ongoing debate about creating a new, formalised Norwegian language.
We ended up with two, but one of them - bokmål - was basically Danish + Norwegian pronunciation + various spelling reforms, as this was effectively what was spoken amongst the upper classes in the cities, and this (with further spelling reforms) is the dominant written language today (the other was based on spoken dialects, and is further from Danish but not that much) .
So we've "only" had about 200 years for the languages to diverge again.