According to an article I came across today, researchers at the University of Oslo believe that English is descended from Old Norse and not from Old English as it is closer in terms of grammar to the modern Scandinavian languages than to the West Germanic languages such as Dutch and German. They say that Old English or Anglo-Saxon is very different from modern English, and believe that Old English died out while Old Norse developed into modern English, with influence from Old English, which is the opposite to the standard model. English grammar and word order certainly has changed a lot over time.
I’m not sure how they came to these conclusions, but I am sceptical. There certainly was Old Norse influence on the dialects spoken in areas of Norse settlement, such as the north of England, and I’ve heard that north eastern varieties of English, such as Geordie, are phonologically similar to Danish.