The author objects to this point:
Many times within the text Peter Heather contends that the centuries long linguistic continuity of particular Germanic tribes … necessarily entails that the barbarians had to have brought women on their migrations.The key is that Germanic languages clearly continued to be transmitted:
Someone with a better grasp of the details of sociolinguistics can enlighten us on the exact details of how language is transmitted, but I’m rather sure that women are not a necessary precondition for linguistic continuity.I'll leave more detailed discussion to actual sociolinguists and historical linguists (I hope one of our contributors might actually read the book and report!), but these are interesting questions. Certainly a language can be maintained in some form under those conditions but that is typically a good situation for big restructuring — 'mixed' languages can be created, for instance. A community where the men are mostly speakers of one language and the women mostly speakers of another might be the kind of scenario that would lead to the structural differences that English shows from the rest of Germanic.
My point here is simply that somebody interested in socio-historical linguistics might want to look at Heather's book and see whether it opens the door to a fresh analysis of parts of Germanic history.
(Map from the fantastic University of Texas collection, here. Because I like old maps. Click to enlarge.)