After the Roman legions left England the Romano-British were left to their own devices, which would have been fine except for one thing, there were plenty of others willing to take their place, Picts in the north and Saxons on the East. “Saxons” incidentally didn't come from “Saxony”, the word was used much as European settlers described the diverse Native American tribes as “Indians”. In fact “Saxons” covers many different Germanic tribes. There was also no “Britain” as such, or even “England”, as authority broke down. What does seem clear is that the leader opposing the Saxons was called Vortigern.
Vortigern is a bit of a shadowy figure, not least because most of the sources we have now were written by Saxon writers, and even then many years after the event. Whether is was some sort of overlord of the Britons, or just a local ruler in the south east, he at least controlled the richest region in England, and thus the most tempting target. His response was to hire mercenaries. In 449 he invited a a group of Jutes, from Jutland in Denmark, to serve under his command, giving in return the Isle of Thanet for their use (under his sovereignty of course). The tribal leader, Hengist, agreed. And it worked, Hengist and his brother Horsa, beating off raiders whilst their families built up a settlement on Thanet (basically the eastern tip of Kent around Margate, which was actually an island at the time). In fact, it worked so well that Vortigern offered to marry their sister Rowena, cementing ties between the two groups.
Hengist was a bit more ambitious than that. He had seen at close hand how rich, and vulnerable, Vortigern's state was and he hatched a plan. This plan, according to legend, consisted of agreeing to the wedding and when the British party arrived, including of course all the important people in the state, he would butcher then and decapitate the establishment. The plan failed, Vortigern and his brother Catigern, managing to escape with their lives. The stage was now set for a short and bitter civil war, Vortigern raised an army and returned, burning with vengeance.
Details are vague and contradictory, but a good summary of current ideas is at deadliestblogpage.wordpress.com/2012/03/22/the-age-of-arthur-part-4/
The Romano British saw themselves as the inheritors of Roman civilisation, defending themselves against barbarians. In the north there were well established legionary settlements, including possibly the descendants of Samaritan heavy cavalry, and firm alliances with local tribes, Unfortunately, in the south there was neither, and defence rested on local levies. Some of the old Roman coastal forts were still strong, but society was not especially martial.
Vortigern probably had a bodyguard of about 150-300 men, the Bucellarii or Teulu, looking similar to Roman light cavalry with mail shirts, swords and javelins. These would have been good troops. But the bulk of his force would have been local levies, organised and armed as a cut-price version of the Legions, in units of 100 with a shield, spear and javelin, but lacking the training or iron discipline of the Romans.
The Saxons were a different force entirely, more akin to pirates, or doubtless adventurers in their own minds. Most in this case came from Hengist's homeland of Jutland, though not necessarily all, as he was already known throughput the Germanic world.
Like the British, the core of the army was a body guard of several hundred men, the “comitatus” or “gesith”, and these were probably the first to arrive. But as words spread of Hengist's successes men swarmed across to join him in Kent.
The “Saxons” were “men with seaxes”, a type of large knife, and this seems to have been a signature weapon, though most had a spear and a circular shield with an iron boss. The wealthy or important had mail shirts, and often a broadsword. And all were professional warriors, more than a match, man to man, for most of the British they would face in southern England.
Again, what happens next is disputed (well, this is the “Dark” ages). But a rough approximation is that, after several skirmishes, the two sides met in 455 at a ford on the river Medway, at Aylesford. The river Medway divides Kent east/ west, with presumably the Saxons arriving from the east, from their base in Thanet, and Vortigern arriving from his territories to the west. Details are unclear, but it seems to have been hard fought, with Horsa and Catigern both falling, and the Saxons being driven back towards Thanet. More skirmishes followed, with a huge battle at Crayford in 457 which according to the Anglo Saxon Chronicle was a Saxon victory, although by 466 Vortigern's son Vortimer had almost driven Hengist into the sea, with a climatic battle at Ebbsfleet (“Wippedesfleote”) near Ramsgate. Here Vortimer was killed, and in the resulting power vacuum the Saxons stormed back, finally establishing complete control. Hengist, and his son Oisc, invited more settlers from back home and established them to the west of the Medway, keeping the East for his own tribe.
The “country” Hengist set up became known as Kent, using his family banner of a prancing white horse on a red background (“Hengist” being “stallion” in Old German). It remained as an independent state, more or less, for over 300 years until it was finally annexed by Mercia in 785.