They've never left. They arrived in the 5th century and became part of the "English" in the 9th/10th century. The period of their rule came to an end with the Norman invasion of 1066 but like much of the nations mongrel history they just merged becoming Anglo-Norman. While the ruling class was Norman and then Anglo Norman the underlying people were considered mostly descended from Anglo saxon (although Jutes, Norse and Celts are all mixed in there as well) and the term has stayed with England.
As you can see from the above, we're just a crazy mixed-up, yet fantastic nation!
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They didn't because England did not exist and they did not inhabit what is England today.
Saxons were/are from Saxony. Anglo-Saxons are in the Uk, a combination of the Saxons and the Angles.
The Roman did not fight the Anglo-Saxons. The merging of the native Saxon culture and that of the conquering Germanic tribes did not occur until long after the Roman empire with drew from Britannia.
England was at one time inhabited by a tribe called the Angles, and then England was invaded by a Germanic tribe called the Saxons, and as these two ethnic groups gradually merged, they became the Anglo-Saxons.
410
totes bro