Gildas
The 6th-century historian Gildas wrote De Excidio et Conquestu Britanniae (English: On the Ruin and Conquest of Britain) in the first decades of the sixth century. In Chapter 23, he tells how "all the councillors, together with that proud usurper" made the mistake of inviting "the fierce and impious Saxons" to settle in Britain. According to Gildas, apparently, a small group came at first and was settled "on the eastern side of the island, by the invitation of the unlucky usurper". This small group invited more of their countrymen to join them, and the colony grew. Eventually the Saxons demanded that "their monthly allotments" be increased and, when their demands were eventually refused, broke their treaty and plundered the lands of the Romano-British.
It is not clear whether Gildas used the name Vortigern. Most editions published today omit the name. Two manuscripts name him: MS. A (Avranches MS 162, 12th-century), refers to Uortigerno; and Mommsen's MS. X (Cambridge University Library MS. Ff. I.27) (13th-century) calls him Gurthigerno. Gildas adds several small details that suggest either he or his source received at least part of the story from the Anglo-Saxons. The first is when he describes the size of the initial party of Saxons, he states that they came in three cyulis (or "keels"), "as they call ships of war". This may be the earliest recovered word of English. The second detail is that he repeats that the visiting Saxons were "foretold by a certain soothsayer among them, that they should occupy the country to which they were sailing three hundred years, and half of that time, a hundred and fifty years, should plunder and despoil the same." Both of these details are unlikely to have been invented by a Roman or Celtic source.
Gildas never addresses Vortigern as the king of Britain. He is termed an usurper (tyrannus), but not solely responsible for inviting the Saxons. To the contrary, he is supported/supporting a "Council", which may be a government based on the representatives of all the "cities" (civitates) or a part thereof. Gildas also does not see Vortigern as bad; he just qualifies him as "unlucky" (infaustus) and lacking judgement, which is understandable, as these mercenaries proved to be faithless.
Modern scholars have debated the various details of Gildas' story, and attempted to pry open his language after more information. One point of discussion has been over the words Gildas uses to describe the Saxon's subsidies (annonas, epimenia), and whether they are legal terms used in a treaty of foederati, a late Roman political practice of settling allied barbarian peoples within the boundaries of the Empire to furnish troops to aid in the defence of the Empire. It is not known whether private individuals imitated this practice. It is also not known whether Gildas' reference to "the eastern side of the island" refers to Kent, East Anglia, Northumbria, or the entire east coast of Britain. Gildas describes how their raids took them "sea to sea, heaped up by the eastern band of impious men; and as it devastated all the neighbouring cities and lands, did not cease after it had been kindled, until it burnt nearly the whole surface of the island, and licked the western ocean with its red and savage tongue" (chapter 24).
The only certainty one gets, after reading much of the secondary literature, is that even the writers close to Gildas in time struggled with the gaps in his account, which they filled with either their own research, or imagination.