The Jutes, Angles and Saxons invaded from the Continent. The Irish invaded across the Irish Sea. The Britons north of Hadrianís Wall set up their own client states and kingdoms. This meant that there were many kingdoms extant during the Age of Arthur.
Basically, here is a quick overview - I have more details back in Ireland, but that is no use here.
The Saxons created kingdoms in the South of England (Essex, Sussex) and the Isle of Wight, Southampton.
The Jutes created a kingdom in Kent (I saw a documentary years ago on language and they played a recording of a man from Kent speaking in his local dialect, made in 1890 or thereabouts. They then played a recording of someone from Fresia saying the same thing in Fresian - it was virtually identical, something which has stayed with me ever since.)
The Scots created the Kingdom of Dalriada, based around the Western Isles, and several kingdoms in Wales and Cornwall.
The British Tribes created many kingdoms in Devon and Cornwall, in Strathclyde and Cumbria, in North and South Wales, in Orkney and in Brittany.
The Picts did not create any kingdoms in Roman Britain, but had their own kingdom in Caledonia which, incidentally had the largest fleet in Britain, so much for "Painted Savages".
These kingdoms were continually at war with one another and it was not just Britons vs Saxons or Britons vs Irish, quite often it was Briton vs Briton with Saxon or Scottish allies. The patchwork nature of these kingdoms meant that alliances were forged and broken regularly and that kings rose and fell very quickly. Over the next two hundred years, the kingdoms were consolidated into a few larger kingdoms and everything was a lot clearer. However, during the Age of Arthur there is a great deal of confusion.
This is ideal as the GM can rewrite history to make it fit what he needs, especially when a king such as Arthur appears to unite the kingdoms. He can start with Wales and Cornwall, then bring in The Men of The North, conquering the nearby Saxon kingdoms, then the Scottish kingdoms in Wales, or perhaps via marriage, one school of thought, which I favour, says that Guinevere was an Irish Princess. Finally, he can drive the rest of the Saxon kingdoms away, forcing them to unite under his banner. Once Britain is united, he can move against the Continent, attacking the Jutes and Angles and conquering Scandinavia. We know that he attacked Brittany to fight Lancelot, so he could have territorial ambitions there too. I see Arthur as trying to rekindle the Age of Rome and become a new Emperor.