The maps on Wiki suggest that the Angles, Jutes and Saxons lived next door to each other in Denmark and north eastern Germany to the Dutch border.
Which suggests that their languages were the same. Danish or some sort of Germano Danish. Dutch is too far removed from Danish to be a close relative. The Anglo Saxon chronicles are written in what we are told is Anglo Saxon which must be close to Danish. Beowulf is said to be very close to Danish and is set in Denmark which suggests relationship between Anglo Saxon and Danish.
https://en.wikipedia.org/wiki/Saxons
https://en.wikipedia.org/wiki/Jutes
If this is true then it is apparent that the language of England, English, was not the language of that area of Denmark unless it really was Anglo Saxon and underwent a dramatic change after the Normans invaded.
Whatever the three groups were up to on the continent has no bearing on the English language in England and for that matter Scotland.
The Danes were and always were part of the Scandinavian group of languages well into the later middle ages and beyond.
If these three groups did settle in England their languages may have formed part of the language of an elite aristocracy but with the advent of Latin, another elite language, and then Norman French a third elite language the 'Angle, Saxon and Jutish' elite associated themselves with the latter two languages and left their ancestral languages behind. Leaving the serfs and villeins to carry on with their own language as they had always done.