During the 3rd century there was a massive dying off in the contemporary empires (Rome, Parthia, India, Han China) thanks to one or more plagues. The same scourge hit the barbarians as well, which delayed the total collapse of Rome’s border barriers.
During the fragmented rule of various overlapping emperors, the Romans had at least a temporary rule in Jutland (basically, modern Denmark; a rescue dig in Copenhagen, during early phase of some construction, turned up a Roman cemetery); the forests of Jutland were cleared during that time. This probably took place during the few years of the probably illiterate Emperor Maximinus Thrax, as traces of a large battle dating to his time were excavated not many years ago in n Germany.
Taking centuries, the forests grew back in time for Svein Forkbeard’s 20 year preparations for his invasion of England. He needed timber for barracks and ships.
It could be that Roman withdrawal from Jutland opened the door for Angles, Saxons, and Jutes to issue forth from the Baltic. OTOH, the Saxon Shore was a Roman command spanning both sides of the Channel, because various non-Roman groups merely arrived overland in mass migrations, possibly into already emptied or sparsely populated lands, while fleeing the plague in their own homelands to the east.
The climate cooled as well — 100 percent naturally — and as with the much more recent Little Ice Age, some of the population collapse could very well have stemmed from crop failures as the planting practices didn’t keep pace with the cold rainy conditions.
Of course, everything had to unfold the way that it did to lead to the result we see, which includes, we all got born.
Well, I do approve of that. :)