The facts that started the legend of King Arthur are:
1) Arthur was a man that lived and led in Britain.
2) Arthur never called himself a king.
3) Arthur loved his dog.
Some of the descendants of Arthur have put together a plausible family tree. The lineage from King Clodius II through King Somerled of the Isles is historically documented.
The other historical background started with Gildas, Nennius, and the Annales Cambriae. Arthur's name also appears in quite a few poetic sources including Y Gododdin and Lord Alfie's Tennyson.
The legendary Arthur developed as a mythical character largely through the popularity of Geoffrey of Monmouth's 12th-century Historia Regum Britanniae (History of the Kings of Britain).
Geoffrey developed Arthur as a king of Britain who defeated the Saxons and established an empire over the British Isles, Iceland, Norway, and Gaul. Many of the characters associated with Arthur appear in Geoffrey's work including: Arthur's father, Uther Pendragon; his scientist and adviser, Merlin; the sword, Excalibur; his birth at Tintagel; and his death at Avalon. Lancelot and the Holy Grail first appear in the 12th-century French writer Chrétien de Troyes work.
The round table is an important element of the King Arthur legend. Since Arthur didn't consider himself a king or supreme being, he did not want to sit at the head of the table. Instead, he wanted a level playing field and had the entire team sit around a round table. The concept of a "round table" discussion still exists in modern business philosophy.