How old is English?
 In fact, as the German-speaking east of Britain traditionally followed the north European way of doing things, Anglo-Saxon warriors had been engaged since the 3th century. They were few in numbers. We can consider them as some local policemen during that period. It's only after Honorius' letter that the hiring of Anglo-Saxons increased dramatically.
 The word 'orientali parte' is important as it suggests also a western part. For me it's clear that Gildas mentioned the existence of 2 parts: east where the proto-English lived and west where the 'real Britons' (Welshmen) lived.
What Vortigern did was to rubber-stamp officially the hiring of Anglo-Saxons, as they proved to be valid soldiers, but he added more organization and control. This was the Adventus Saxonum and it happened with the approval of omnes consiliarii, all consultants (=members of the council). The hiring of fully qualified warriors now became the official aim. The German candidates had to be approved, selected, trained, and only then appointed to their final destination. At the same time, a new, official message was sent to North-Germany: Britain needed the best and only the best. As a counterpart, higher wages were promised for whom would match the requirements. The coming of the Anglo-Saxons became well organized. This proves that Britain was still capable of organizing things centrally, on a national level. There is a possibility of an intention to form a new central army with Anglo-Saxons, but commanded by the British senate, as some sort of counter weight for the increasing power of some local lords .
In 428 a certain Hengest-the-Jute came with the 3 reported ‘keels’ of men, estimated at some 75 warriors in total. He probably landed in London. People must have remembered that Hengest was amidst the first to be welcomed officially. Hengest was at that moment an ex-officer from the guard of the late Hnaef the Dane (see the Finnesburgh fragment - Beowulf). He was probably in his early thirties. His former position made possible to appoint him as one of the officers of the new selection and training committee. It is unlikely that Hengest immediately obtained a top-ranking position. The isle (today: peninsula) of Thanet, today Ramsgate - Margate on the east Kentish coast, became the official place of reception for the new arrivals. It must have been the first place in Britain where Hengest was sent to.
The men on Thanet were probably paid by the lords who still had a shortage of Anglo-Saxon warriors or housecarls. As soon as most had sufficient 'stock', the 'Thanet system' was abandoned. At that moment, Hengest and his men probably joined the Kentish upper-class leader(s).
" primum in orientali parte
insulae iubente infausto tyranno ...." 
The mixed composition of the 'Saxon'  led home guards would later (441, the rebellion) become a source of considerable troubles. Anyhow, in the beginning, the new soldiers soon proved, according to Gildas, to be effective in combating the annoying Picts and Scots (Irish) in the North and Northwest. Britain had temporarily dropped the classic central army idea in favour of the north German tradition of hiring skilled members of a warrior class at the service of local lords.
Who fought who?
As societies often do during periods of war, east Britain over-equipped itself in men. Raids had diminished rapidly. Peace came back. This caused a number of Anglo-Saxons to become redundant, especially people of lower quality. As these people fell without work and income, they would join the rebellion of 441.
Nearly all sources suggest that the Brito-Welsh fought some sort of Anglo-Saxon force. On the other hand, nobody reports a classic conquest, what a central-led army is supposed to do. For instance, no conquest of North-England or the Midlands was mentioned. Only some skirmishes in southeast England. The contrast with the conquest of Gaul by the Franks can't be greater. Gaul was conquered in 3 important battles. The Frank army was hierarchical and had a strong leader: Clovis. Very classic. No so in Britain.
How Gildas reports the alleged take-over of Britain is very confusing. Leadership is at best vague. Gildas never mentioned any tribe except Saxons. The notion 'tribe' must have been really old fashioned and was about to be replaced by kingdoms. The tribe of the Dobunni was replaced by the kingdom of Wessex, which corresponded more or less with the ancient tribal territory. Nobody is sure who really was in charge. For Gildas, the enemies were simply bloodthirsty 'Saxons'. The suggested role of Vortigern is to say at least, ambiguous. It's clear that Gildas definitely wants to blame him, however, with not enough proof.
A take-over of all of England supposes
a well coordinated action. It requires a well
organized army, a hierarchy, a clear leadership. None
of that is reported. In fact, we know that the
Anglo-Saxons consisted out of people of various
origins (Saxons, Angles, Fries, Jutes and maybe
more..). The Finnsburgh fragment makes us clear that
those 'tribes' were not always friendly with each
other in their homeland. This is not a single tribe
conquering a country, unlike what happened in Gaul,
unlike the conquest of Britain by the Romans or by
William the Conqueror. So, the most logical solution
to the problem is that the Anglo-Saxons were very much
spread, divided along former tribal boundaries, hence
later the appearance of many small kingdoms but also
occasional small concentrations of 'Saxon' soldiers in
Britain during the 5th century. These forces must have
been too small to achieve a classic conquest of the
whole country. It was most probably not meant to do
so. Also striking is that at no given moment during
the 6th century, the small Anglo-Saxon 'kingdoms'
united to conquer the west of Britain. They were too
busy to fight each other.