Upvote:2
The answer appears to be yes, according to sources such as this: http://en.wikipedia.org/wiki/Migration_Period
Pressure from the Huns apparently "induced" the Germanic tribes to do what they basically wanted to do anyway: head for warmer climes in the south and west. Following the victory of Arminius in 9 A.D., the Germans began to "push back" the Romans away from their homeland. Three centuries or so later, Hun pressure to their rear put the Germans on a "short fuse," with any "mistreatment" by the Romans, real or perceived. By this time, the Germans feared the Huns more than the Romans.
Upvote:8
According to Gibbon, The first "barbaric" nation that permanently settled on the soil of the Roman Empire were Visigoths with the permission of the Roman emperor Valens. The sole reason they asked to move south of the Danube was escaping the Huns - I guess that answers your question.
Upvote:11
Interesting. My first instinct was to tell you the Huns and the Anglo-Saxons weren't contemporaneous, but it turns out they were.
The Huns were active players from about 130 to 453 CE. They enslaved the nearest german tribes (most notably the eastern Goths, aka: Ostragoths), and pushed a lot of the rest into Roman territory. Their own armies at one point (451) made it as far West as Orleans.
To say that they were a major factor in the German invasions of the Roman empire is if anything understating things. While adventurous German tribes like the Ostragoths could expand eastward, there wasn't a big problem between the two peoples. However, in about 370 the Huns rose up, enslaved the eastern German tribes (including the Ostragoths), and all the remaining German tribes ended up huddled together in a little strip of central Europe between the two empires. They clearly couldn't stay there, and frankly attacking Rome was much less forbidding than attacking the Huns (and their German clients).
The Anglo-Saxon migrations started happening around the 400's. Considering the Jutes and Angles completely disappeared from their homelands (replaced by Danes), it might be reasonable to assume they were pushed by something or someone.
Based on all this, I could see (and in some cases have heard) the following possible arguments:
There are a lot more theories floating around, but these seem the best supported.