Are you familiar with the Danelaw, and with Danegeld? I think that knowing "Danes" ruled much of mainland Britain for hundreds of years and provided kings of a unified-ish (pre-Norman) England (Cnut [Canute]) makes it less surprising?
The pronunciation of words between English and Dutch make them appear to be quite different. Once you’re used to hearing Dutch, which most British won’t be, the differences are much, much less than one might imagine.