If you have a look at the following two Wikipedia articles:http://en.wikipedia.org/wiki/Old_High_Germanhttp://en.wikipedia.org/wiki/Old_English_language
you will see that the two languages probably started to diverge in earnest around 500 AD
But it also becomes clear that only very few written material is available today from that period, and because of this there are considerable uncertainties involved.
Put on top of that a lot of people wandering all over Europe
in those centuries, and your question probably becomes quite impossible to answer...