King Arthur is a fictional character. He did not really exist. There is no contemporary record of such a reign. Real kings tend to leave some evidence of their existence behind them, but Arthur apparently minted no coins and issued no charters. He is not mentioned by early historians such as Gildas or Bede, nor is there any reference to him in the Anglo-Saxon Chronicle.
The evidence for his supposed existence is exceptionally slight. A recent book (The Anglo-Saxons, by James Campbell, Eric John, & Patrick Wormald) listed it as follows:
1. An early Welsh poem, which mentions that some hero WASN’T Arthur (“he fed black ravens on the ramparts, although he was not Arthur”).
2. The historian Nennius, who listed twelve battles supposedly fought by Arthur.
3. The Welsh Annals, which mention some of the same battles, and record his death in 537, in battle with Modred.
Nennius wrote his Historia Britonum around 858, which is about 300 years after the events he describes. That is the equivalent of someone writing today about the reign of Queen Anne. Either he had access to written sources that no-one else has ever seen (unlikely), or he used his imagination (more probable). His book can be read on-line at
http://www.thelatinlibrary.com/histbrit.html. Nennius did not call Arthur a king, just “dux bellorum” (war leader). The paragraph about Arthur is sandwiched incongruously between a Life of Saint Patrick (also imaginary) and a set of Anglo-Saxon genealogies, tracing the ancestry of kings back to the (non existent) god Woden. The book seems to have been thrown together from scraps, without much care or understanding.
The Welsh Annals were probably composed at an even later date. The earliest surviving manuscript dates from the late tenth or early eleventh century, and lists events up to 977. So, in this form, it must be at least 400 years later than the supposed reign of Arthur. In the annal recording his death, Arthur is referred to as “the famous Arthur, King of the Britons”, which looks more like a late interpolation than a contemporary description.
The most elaborate account of his reign was concocted by Geoffrey of Monmouth, writing in the twelfth century. His book contains more fiction than fact, and is altogether too bizarre to take seriously. William of Newburgh, writing around 1190, concluded “It is quite clear that everything this man wrote about Arthur and his successors, or indeed about his predecessors from Vortigern onwards, was made up, partly by himself, and partly by others, either from an inordinate love of lying, or for the sake of pleasing the Welsh”.
In 1191 the monks of Glastonbury claimed to have found a tomb with the inscription “Hic jacet sepultus inclitus rex Arturius” (“Here lies buried the famous King Arthur”). No doubt they hoped to boost the tourist trade.
In addition to these, Arthur is mentioned in a Life of Gildas (Vitae Gildae), composed in the thirteenth century. Arthur is said to have killed the brother of Gildas. But Gildas himself criticized five supposedly evil kings
http://www.fordham.edu/halsall/basis/gildas-full.html , but failed to mention the alleged killer of his brother.
The name Arthur isn’t even Celtic, and therefore it does not occur in early Celtic inscriptions or other records. The name is Roman, Artorius, and to find the famous Arthur it is Roman sources that must be examined, such as Juvenal:
“Farewell my country! Let Artorius live there, and Catulus; let those remain who turn black into white, to whom it comes easy to take contracts for temples, rivers or harbours, for draining floods, or carrying corpses to the pyre, or to put up slaves for sale under the authority of the spear.These men once were horn-blowers, who went the round of every provincial show, and whose puffed-out cheeks were known in every village; to-day they hold shows of their own, and win applause by slaying whomsoever the mob with a turn of the thumb bids them slay; from that they go back to contract for cesspools, and why not for any kind of thing, seeing that they are of the kind that Fortune raises from the gutter to the mighty places of earth whenever she wishes to enjoy a laugh?”