The notion that Arthur was some sort of emperor has its origins in the Middle Ages. Geoffrey of Monmouth, in his Historia Regum Britanniae, has Arthur as the ruler of an empire that exceeded Britain and covered parts of Brittany, Ireland, Iceland, Gaul and Norway. Not many modern scholars would accept that this was historically true.
There is no grounds to believe that a British leader beat the Saxon invaders at Badon, resurrected a Roman form of government with its institutions, united the whole country, and kept it united for another 30 years or so, until he died.
He would have been the last Roman emperor in the west, and the first medieval king of the country now called England. There is no archeological or literary evidence for this. Nothing points to anything other than the dissolution of Britain into small feuding units after the Roman withdrawl.