How is it that the Anglo-Saxons were able to take control of Britain ahead of other barbarian tribes?

Interesting question, very!
I have never liked the idea of Anglo Saxon Invasion, Brutal War, and ethic cleansing and slavery?

Now there is another theory that is being developed and that is, the Anglo Saxons were migrants who were settled in this country when Britain was connected to the Continent and had retained their own customs and Language?

Not being an expert because I wasn't there, I have to read up on the subject and we find a lot of pointers to back the later theory up! This theory, leads to the idea that instead of being this terrible blood purge with massacres and people being driven in to Wales and France, there was a change of political leadership from Celtic Romanised Cities to the Anglo Saxon idea of a farming community! A few years ago there was a survey or study of DNA and if I remember aright there is an average of 68% DNA in most of us is Celtic. Considering that all North of England appears to be either Scots or Irish? So much for ethnic cleansing!
This isn't to say there were no wars or struggles, we know that there were, but according to archeologists, there is not a lot to sustain the Saxon Invasion theory!
Hope you find this as interesting as I do.