My growing understanding of the title "King" was that it was originally an ethno-tribal appelation, given to the chief ruler of a folk-nation or People (i.e. King of the Lombards, King of the Franks, etc). I understand, in that way, Charlemagne who was King of the Franks in his own right made other kings his vassals and is therefore an Emperor. Why then did King Alfred of Wessex, who sought to unite the various Saxon kingdoms of England under his crown, not claim the title of an Emperor? Was it because he sought to unite the Kingdoms into one royal realm, under a single King?
Nowadays we understand emperors to be men ruling over a multitude of kingdoms or simply ethnically different people from their own ethnic background.
In the European middle ages on the other hand emperorship was strictly tied to the Roman legacy hence there could only be one emperor per say: the Roman emperor. Western Europe identified this title with the mostly German Holy Roman empire rulers while in the east what we now call the byzantines believed the Basileus ruling from Constantinople to be the legitimate Roman emperor aka the legittimate successor to the Roman empire of old.
Alfred of Wessex therefore couldn't use the title of emperor since the only legittimate emperor, the Roman emperor, were to him Charlemagne's progeny in mainland Europe crowned by the Pope starting from 800 c.e., the idea of Alfred titling himself "emperor" couldn't have possibly cross his mind. At best he could have described himself to be "Kings of the Britons" or "King of the English kingdoms" (since modern day England was splitted in many different petty kingdoms st the time) but not emperor.