I have been reading "Barbarians to Angels" by Peter S. Wells and in it he explained that over the past 30 years, the idea of an Anglo-Saxon invasion of England, and too of a mass migration of Germanic peoples to the island during the 5th Century, has changed due to the lack of significant archaeological evidence that would indicate an arrival of new people's from the continent. What then was the influence for English to become a language of Germanic origin if the island was left with people of Celtic origin? Is it just that the scale of these migrations have been reconsidered? Or have the previous works of earlier English writers such as Bede and Gildas left us with an entirely distorted idea of the Island's ethnic and linguistic evolution?
The idea of mass migration isn't very popular (some accounts go as low as 20-40,000 now), but it's very clear that the language transition went from Celtic to OE quite quickly (probably by 570AD) - we've only got about 20 Celtic words in use (most of which are geographically related). Because of the lack of written work, it all has to be extrapolated back from things like place-names. So the reality is that we had Celtic languages and very quickly didn't, so why?
When languages come into contact, unless they are maintained at the same level, one will be esteemed higher than the other (superstrate vs substrate). Indigenous populations will adopt the superstrate language but superstrate speakers will not adopt the substrate (which is why we've only got 20 Celtic words). So Old English is a prestige language that people want to adopt (because of the prestige aspects - social etc.,), so you don't need mass migration, you just need the resident population to want it. This is what happened.
Or have the previous works of earlier English writers such as Bede and Gildas left us with an entirely distorted idea of the Island's ethnic and linguistic evolution?
They are exaggerated, but at their core are probably good enough - Jutes, Angles and Saxons did come over, how many might be another issue.