Considering the Anglo-Saxons came to England from the Jutes, Angles, and Saxons, I assume they share a common ancestry with the Vikings who later would settle and raid there as well.
How similar where the languages of these peoples? Considering German and English and Dutch today are very similar, and that German is also somewhat similar with Danish, Norwegian and Swedish, it makes me curious how different the linguistics of the Anglo-Saxons was from the Old Norse tongue at the time of their conflicts.
The groups the Anglo-Saxons descended from were more Germanic than Norse. The Anglo-Saxon homeland was in what's now northern Germany - close to the viking homelands of modern Denmark and Sweden, but not actually in them.
Anglo-Saxon and Old Norse were both members of the Germanic language group, but they wouldn't have been mutually intelligible. It'd be broadly similar to a modern German person and a modern British person trying to communicate in their own native languages - there might be the odd word that one understood, but not much more.
Source: Simon Schama's History of Britain