Vortigern is typically thought of as ruler of all of (sub) Roman Britain through the middle half the fifth century. In reality, this is most implausible. When the Roman Legions left in 409, Britain has been divided into four Provinces for over a century; there is no evidence behind the unification assumption.
As Roman power weakened, prevalent conditions in western Europe pulled towards small kingdoms. Only from the seventh century onwards did Britain’s small kingdoms start to habitually become overrun by bigger ones.
It is surely significant that historical evidence linked to Vortigern and his son Vortimer identifies several battles against Saxons in Kent, one of which resulted in a retreat to London, concessions to Saxon control (at different times) of Thanet, all of Kent, and Sussex and Essex, and a victory over Britonnic rival Ambrosius at Wallop in Hampshire; but that the only other recorded location of either political or military activity for Vortigern or Vortimer is Belgium, where, having driven the Saxons out of Britain completely, Vortimer arrived with 10,000 men and was disastrously defeated. (This expedition in c468 makes Vortimer, I suggest, the prime candidate for the mysterious Riothamus, “Thames king”.)
This geographical pattern is indicative of the area controlled by Vortigern having been the Province of Maxima Caesariensis. There is room for argument about that Province’s exact boundaries – I argue that the northern boundary was close to that of present-day Oxfordshire and Northamptonshire and thence to the Wash, see my post of 31st March 2013 on “Gildas’s 28 Cities”,  – but certainly the major part of the Province was all the parts of Britain just mentioned.
Another sign pointing in the same direction is that although Vortigern won the Battle of Wallop in 428, the record says he remained afraid of Ambrosius. This only makes coherent sense if Ambrosius had a power base elsewhere in Britain than Vortigern’s and substantial enough for him to be a threat to Vortigern.
Nothing is directly known about this Ambrosius. What is known is that according to Gildas, half a century later another Ambrosius, Ambrosius Aurelianus, became a powerful leader somewhere in Britain; and that at the time of Gildas’s writing, c530, his grandson Cynan was a king in western Britain. Combining the works of Gildas and Taliesin enables Cynan’s kingdom to be identified as Powys, which was the successor state to the Roman civitas (city-district) centred on Wroxeter. It approximately corresponded to Staffordshire, Shropshire, Cheshire, Montgomeryshire, and Radnorshire. Another scion of this family prominent in the historical record is the sixth century Christian leader Pol Aurelian, who studied at St. Illtyd’s seminary at Llan Illtyd Fawr (now Glamorgan; then in the Kingdom of Gwent), strengthened the structure of the Old Church at Glastonbury Abbey, and founded the monastery at Leon, Brittany, where he became known as St. Pol de Leon. Considering this geographical provenance in his lineage, it is a reasonable possibility that the Ambrosius who was a forbear of these Aurelians and a potential threat to Vortigern was a, perhaps the primary, ruler in western Britannia, i.e. of the Province of Britannia Prima. Roman Britannia Prima included everything from the civitas of Wroxeter and those of Cirencester, Ilchester, and Dorchester, westwards.
Place names derived from Ambrosius are suggestive of Ambrosius Aurelianus’s spheres of governance and of combat. Several are in Britannia Prima: one in SE Wales; others in the southeast of the province – Worcestershire, and Amberley near Stroud. One, Amesbury, is just on the Maxima side of the provincial boundary which ran across Salisbury Plain. These scattered ‘Ambros’ place names are consistent with the supposition that Ambrosius’s powerbase was the Aurelian heartland of Britannia Prima.
Several other Ambros- names form a line running more-or-less SW to NE from Amersham. By the time Ambrosius Aurelianus came to power (in 479 according to one of the Irish annals), most of the former Province of Maxima Caesariensis had passed into Saxon control. The exceptions were the Silchester civitas (approximately north Hampshire and pre-1974 Berkshire), which emerges into post-Roman history as the ambiguously Saxo-Britonnic kingdom of the Gewissae – cf my identifying the true location of Netley and Cerdic’s earliest conquests on the north bank of the Thames near Oxford in my post of 7th June 2014 ; and the civitas-becoming-kingdom of the tribe known to the Romans as the Catuvellauni.
This kingdom is known later on as Calchfynydd in Welsh, and as Cilternsaetna in Anglian English, its name recorded in the Mercian Tribal Hidage of c672; both words denote ‘the people of the chalk hills’, i.e. the Chilterns. It was a substantial kingdom ruled by Britonnic kings until it was defeated at the Battle of Bedford in 571; it will have been reduced to at most a rump by the further defeat in 580 at Bannaventa (the Roman walled town near Weedon Bec in Northamptonshire) when King Cadog was slain.
It may be that Ambrosius Aurelianus and these two Britonnic kingdoms worked together in the 480s to contain Anglo-Saxon expansion. The Ambros place-names are along what could well have been the western edge of the English kingdoms of Essex (which included London and can be presumed to have also included what later became Middlesex) and East Anglia, which is suggestive of a line of defence and boundary between those English-controlled territories and Calchfynydd, a boundary which Ambrosius Aurelianus successfully held militarily; a boundary in due course agreed by treaty and respected for the first 70 years of the sixth century.
Besides western Britannia being Aurelian territory and not Vortigern’s, there is also a good indication that another of the four Provinces was not under Vortigern’s suzerainty. There are king-list genealogies in the text Bonedd y Gwyr Gogledd (the Descent of the Men of the North) for various successor kingdoms in what in the fourth century had been Britannia Secunda, the northern Province which included everywhere between Hadrian’s Wall and the Trent except East Yorkshire and (probably) Nottinghamshire. They are all headed by Coel Hen (the king immortalised in nursery rhyme as Old King Cole) and Keneu. The inference is that for a few decades after 409 those two kings held some degree of sovereignty over the whole Province, before kingdoms such as Rheged (based at Carlisle) and Elmet (based at York) became fully separated and de-facto autonomous. None of these genealogies mention Vortigern.
The remaining Province was the relatively small Flavia Caesariensis, which I argue [28 Cities] approximated to East Yorkshire, Nottinghamshire, Derbyshire, easternmost parts of Staffordshire and Warwickshire, Leicestershire, and Lincolnshire. There is brooch evidence of early Anglian warrior presence within this area, but no battles recorded by either Britonnic or Anglo-Saxon sources. In the absence of evidence to the contrary, the hypothesis that the Province passed peacefully into Angle control, maybe indeed as early as before 440, has to be considered credible. The lack of disruption to agricultural practises shown by archaeological exploration at Hessle in East Yorkshire supports the peaceful transition hypothesis.
As has often been said, an absence of evidence is not convincing evidence of absence, least of all in a period as thin on evidence of anything as the fifth century. Nevertheless, three important patterns – the record of Vortigern’s battles and political actions across one Province, Maxima Caesariensis; the absence of evidence of any activities by him in Britannia’s other three civilian Provinces; and the presence of evidence in two of those Provinces of other men in control, and the hint, at least, of Saxon control in the third – point in one direction only. The rational inference is that Vortigern was supreme ruler – in the Roman structure the de-facto Provincial Governor – of Maxima Caesariensis, and only of Maxima Caesariensis.
 My analysis puts East Anglia and the Fens in Maxima. I know of no reason to suppose that Vortigern’s rule extended to those two civitates; it may be that they became effectively Anglo-Saxon ruled within a generation of thedeparture of the Legions.
 See Morris, The Age of Arthur, map p101.
 Or at any rate, most of it. The Roman civitas capital St. Albans and the nearby town of Hertford may have become Anglicised long before the rest of the civitas’s territory including Northamptonshire, Bedfordshire, Buckinghamshire and part of Oxfordshire fell under Anglian rule.
 Morris’s map also shows three Ambros place-names in Sussex and one in Kent. These do not fit tidily into any theory. Perhaps Ambrosius Aurelianus won battles in those areas.
 The Gallic Chronicle of c441 said that Britannia had ‘passed into the hands of the Saxons’. This date is thorny for historians because of Vortigern’s granting rule over Thanet to the Saxon Hengist, after Aetius’s failure to send troops to his aid in 446. That event was presented both by Gildas and by Bede, drawing on Kentish sources, as momentous, not because Saxon warriors like Hengist helping a ruler of Britons was new – they’d been doing so for a century or two – but because the concession of Thanet was seen as the first bit of Anglo-Saxon rule over part of what was to become England, and the thin end of a wedge: thirty years later, all of SE England was under Saxon rule.
Maybe, though, 446 was the watershed “Coming of the Saxons” ONLY in the south-eastern districts ruled by Vortigern. Beyond doubt the Chronicle’s statement was an exaggeration: neither the documentary nor the archaeological evidence suggests any areas of Anglo-Saxon control in two of Britain’s four Provinces at that time, Britannia Prima and Britannia Secunda.
Equally though, I know of no reason to suspect the highly-respected Chronicler of writing nonsense. The region most likely to have been already under Anglo-Saxon control by 440 is the eastern coastal counties from East Yorkshire through Lincolnshire to the Peterborough area and East Anglia, plus lands on either side of the lower Trent, which was the Angles’ original ‘Mierce’ (meaning: borderland, c.f. modern German maerchenland), so named long before ‘Mercia’ came to mean a large Midland kingdom. This region includes West Stow (near Bury St Edmunds), the site of a reconstructed Anglo-Saxon village which is indicated to have been in that location in 440; it also includes Hessle. Two-thirds of it had been in Flavia Province.