From the Historia Brittonum Chapter 50
The first battle in which he was engaged, was at the mouth of the River Gleni
(1).
The second, third, fourth, and fifth, were on another river, by the Britons called Duglas
(2), in the region Linuis.
The sixth, on the River Bassas
(3).
The seventh in the wood Celidon
, which the Britons call Cat Coit Celidon
(4).
The eighth was near Gurnion castle
(5), where Arthur bore the image of the Holy Virgin, mother of God, upon his shoulders, and through the power of our Lord Jesus Christ, and the holy Mary, put the Saxons to flight, and pursued them the whole day with great slaughter.
The ninth was at the City of Legion
, which is called Cair Lion
(6).
The tenth was on the banks of the river Trat Treuroit
(7).
The eleventh was on the mountain Breguoin
, which we call Cat Bregion (8).
The twelfth was a most severe contest, when Arthur penetrated to the Hill of Badon
(9). In this engagement, nine hundred and forty fell by his hand alone, no one but the Lord affording him assistance.
In all these engagements the Britons were successful. For no strength can avail against the will of the Almighty.
To what extent this is history and what extent folklore it is almost impossible to say. What is undeniable is that, sometime in the latter half of the sixth century AD, the native Romano-Britons did fight back against invading Anglo-Saxons.
What the Historia Brittonum does record is at least the metaphorical truth of a long war that stopped the Anglo-Saxons in their tracks. There were certainly battles, although whether they took place in the indicated locations, and indeed whether a gentleman called Arthur had anything to do with them, is impossible to say at present.
Notes on the probable or possible locations of the battles
(1) Probably either at the confluence of the rivers Glen and Till in Northumbria near to the hillfort of Yeavering Bell or the river Glen in Lincolnshire.
(2)Duglas is Welsh for blue-black meaning "blackwater" and Linnius is generally considered to be Lindsey, which is part of Lincolnshire although no one can place a other candidates include the river Duglas, in Lancashire or even the river Dunglas in Lothian.
(3) Bassa, the early British name for Baschurch in Shropshire.
(4) Cat coit celidon; or the Caledonian forest.
(5) Probably Garionenum in Norfolk.
(6)Probably Caerleon near Newport in south Wales although also possibly Chester, also sometimes known as the city of the legion.
(7) Probably the same shores of Tryfrwyd that are mentioned in the poem Pa Gwr yw y Porthor?; not that this helps us much. Suggestions include the river Brue, in Somerset or the Ribble in Lancashire.
(8)Breguoin or Brewyn is the old Welsh or Brythonic name for Bremenium or the Roman fort of Rochester.
(9) Or Mons Badonicus as recorded by Gildas.