The languages of the fifth century Britons evolved from a common Indo-European language dubbed, “Common Celtic.” It was probably imported into Britain beginning around 500 BC with the arrival of migrating Celts. Because no written version of the language and its descendants existed until perhaps AD 500, it is not known what it was called by the people who spoke it.
Common Celtic split into two branches, the British and the Irish. It is theorized that the Irish or Gaelic version, Goidelic (dubbed Q-Celtic) migrated to Ireland, the Isle of Man and Western Scotland; and the British, or Brythonic/Brittonic version (P-Celtic) entered Britain. When this happened is unsure, but it is evidenced in place names and personal names.
Very little is known of the language of the Picts of the far north, but it is speculated it may have been a branch of early Brythonic, closely related to Welsh. Like early Celtic, it is lost and only remains in a few inscribed place names or references in Latin texts to personal names.
With the Roman invasion and occupation, Latin was introduced into Britain. Unlike Gaul, where a version of colloquial Latin was gradually adopted and the native Gaulish tongue lost, Celtic remained the native language and a number of Latin words borrowed into it. Only the aristocracy and Roman migrants spoke Latin, making it exclusively the language of literature and government. The average person could not afford an education in which the tongue could be acquired.
By the fifth century, Brythonic was evolving into the beginnings of early Welsh. Cornish was closely related as well. Fleeing Germanic invaders, migrants to Brittany (Armorica), took their language with them and developed Breton. At that time, the various branches of Brythonic were probably more like dialects. Anyone from the Antonine Wall to the southern coast could be understood by anyone else.
It is not known what the Celtic Britons called their own languages. Celtic is a label applied by later scholars. It is believed that the word Cymry, roughly meaning countryman, began to be used in the sixth century by Welsh speakers to identify themselves as a unit. Conceivably, it could have been in use earlier, but without documentation, discerning this is impossible.
Irish migrants introduced Gaelic into the northern kingdoms of the Picts when they settled in Dal Riada (Argyll) in the later fifth century. Their tribal name, Scoti, gave Scotland its name. Scots Gaelic spread across the north, mostly above the Antonine Wall. As the Picts and Scots merged into a united kingdom called Alba, Pictish was lost to Gaelic.
With the advent of invasions in the fifth century various Germanic languages were introduced into Britain as well. The Britons tended to lump Saxons, Angles, Jutes, and Franks together under the Saxon name, but each group brought their own languages and dialects with them. As their encroachment and subsequent conquest progressed, their Anglo-Saxon tongue evolved into English.
It was not until the monastic movement began in the fifth century that literature and historical events started to be written down. The monks wrote in Latin, but they include personal names and place names. Unfortunately, there were no rules in place for standardization in spelling until, literally, centuries later. Many mistakes in transcriptions and translations have been made over the centuries, as well changes in place names, making identification difficult or impossible. However, without the few surviving works from those monks and clerics, we would know nothing of the Age of Arthur.