which one?
it is hard to pin down an "exact time" or a person/ persons to assign the legend to
problems with written records, etc
there is,though, a lot of written info on "him" and the wars/battles that his legends are based on (the holy grail thing was added in later to get the church's blessing on a patriotic story)
his name and legend/real actions should be relied on the Welsh for the best accuracy. As he was Welsh (a saxon word assigned to any non Saxon Briton that the fought) they would have had the best motivation and probably the best record keeping of the time (as any remaining Roman Britons of note.money would have retreated to what we now call WALES)
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but, reading the history alone can get quite boring; a good historical fiction acct is written in THE WARLORD CHRONICLES by Cornwell. he sues a lot of what is known of late roman and immediate post roman britain's culture and mix of ppl's. he ties in the religious aspect as not a christian one but rather a Druidic quest to gain lost treasure-of which his arthur wants no part.
but then there is the historic/archaelogical. the wiki is pretty good:
and on Ambrosius one of the historical composite candidates: