The King Arthur of history is basically the Arthur mentioned in the Historia Brittonum written about 830 AD and in the Annales Cambriae written about 975.
The HB puts the Twelve Battles of Arthur some time between about 450 and 550 AD, while the AC dates Arthur's victory at Badon in a year corresponding to 516 to 518 and the battle of Camlan where Arthur died in a year corresponding to 537 to 539.
Thus they were written about 292 to 438 years after Arthur allegedly died and it is possible that legendary elements have been added to those accounts.
In late Roman times most of Roman Britain was divided into city states called civitates based on former British tribes. Each city state had elected magistrates and a council and was divided into districts called pagi. Late Roman Britain had four or five provinces whose governors used various titles and supervised the governments of the civitates. The governors were supervised by the Vicar who ruled the diocese of Britain - government diocese, not a religious one.
In Cornwall, in Wales, and between the two walls in the North were British tribes that were not very assimilated to Roman culture and may still have had kings, who no doubt lived more or less peacefully with the local Roman military units and acknowledged the authority of the Emperor just as a number of 19th century Indian tribes lived in peaceful coexistence with local US military units and acknowledged the authority of the Grandfather in Washington.
Beyond the Antonine Wall were the Picts, who may not have been culturally British and were often enemies of Roman Britain.
The Diocese of Britain was part of the Praetorian Prefecture of the Gauls, which was part of the Western Roman Empire.
Post Roman Britain may have continued the Roman system of government and also reverted to Celtic forms of government. Leading men may have made themselves kings of each city state, and each pagus may have had a sub king, thus making maybe more than a hundred sub kings in Britain. So Arthur, who led the kings in battle, was probably at least a sub king in rank. Each province may have been ruled by a second level king, and the whole diocese may have have been ruled by a third level king.
Or city states may have continued to elect magistrates, and governors could have been chosen for each province, and a vicar to rule all the diocese. And maybe the vicar claimed to be loyal to the Roman prefect of Gaul and to the emperor. Or maybe the ruler of Britain claimed to be an emperor, a sort of north western Roman Emperor.
Or maybe the rulers of Britain used both Celtic and Roman titles simultaneously, the ruler of a city state claiming to be both a king and magistrate, and the ruler of a province claiming to be both a second level king and a governor, and so on.
Because there were several provinces in late Roman Britain, Britain was referred to as the Britains politically. Thus the vicar used the title of Vicar of the Britains. And so presumably in Arthur's era the overlord of all post Roman Britain would claim to be king, or vicar, or emperor, or whatever, of the Britains, not of Britain, and not of the Britons, though the title of King of the Britons is used in medieval sources.
The story of the sword in the stone is first mentioned by Robert de Boron in Merlin around 1200 AD. That is about 700 years after the time of Arthur.
And so the Sword in the Stone is considered fictional.