England is a tricky case, because we don't have much in the way of written sources, and archaeology isn't as good for answering polical-administrative questions as it is other lines of inquiry.

What we know is that the last legions left Britain in 410 (probably - the sources for this are pretty sketchy, actually), probably to participate in one of the many civil wars that tore the western empire apart from the inside during the fifth century. After that, we have some tantalizingly sparse evidence thhat Britain stayed in communication with the rest of the Roman world, but the extent is difficult to say. It's quite possible that Britain considered itself to still be a part of the Roman empire for some time after the legions left (Guy Halsall raises the interesting suggestion that high-status art in Britain suddenly looks less Roman right around the 470s, as though the political events in Italy had some significance in britain even then). But we really can't say for sure if whoever filled the administrative gap left by the Roman army - probably the 'Saxon' federates in some regions (who were almost certainly, like other barbarian federate groups, multi-ethnic auxilary troops); perhaps surviving Roman elites, or members of local aristocracies (who would, by this point, have also been Roman, unless they chose to de-emphasize that part of their identity in favor of older local culture, or so ething new like the 'barbarian' cultures north of the Rhine).

Archaeologically, Roman architecture seems to be collapsing by the late fourth century (especially villas). This in itself doesn't meant that Romans disappeared from Britain (many of the abandoned villas weren't very old when they were left to collapse, and Britain had been part of Rome before they were built). But they do suggest that elite Roman culture in Britain was looking really different by the start of the fifth century. This change was relatively independent from the withdrawal of the legions (though it may have contributed to the feeling that they could be better used in civil wars elsewhere), and happened before the Saxon invasions (we have vague references to Saxon pirates attacking England in the fourth century, but it's not clear how much of an actual threat this was - or who exactly these Saxons were (since Romans loved to slap names onto babrbarians that the barbarians might not have used themselves).

Then Britain's economy collapses, for most of the fifth century. This collapse started much earlier (Roman industry in Britain was crumbling since the third century, and the movement of Roman administration away from Trier in the late fourth century seems to have further impoverished the province), and doesn't appear to be connected to barbarian invasions. Indeed, there's no archaeological evidence for an 'invasion' per se- just the normal movement of poor farmers through the fifth century that you always see happening. By the sixth century, when things are slowly romving toward recovery, Britain's material culture looks very different - people live in wooden buildings instead of stone, and elites are buried with weapons and jewelry with artistic styles that look very different from Roman precursors. The demography is a blend of locally born people and immigrants from both the east (Germany/Scandinavia) and west (Wales, perhaps even Ireland).

But this change was gradual, and similar changes were occurring throughout the Roman world. The crucial period for Britain is the fifth century, but the lack of textual sources, and the economic collapse and disappearance of so much of the types of material goods we use to establish chronologies and trace change, make it difficult to know how rapidly the island gave up on being Roman. Certainly by the sixth century, but in Western europe, that's kind of a given.

Many have suggested it was never very Roman to begin with, and that as soon as the legions left the Brittons shouted 'we're free!' The limited evidence available suggests something more complicated, but the precise shape of events is very murky.

Robin Fleming is working on this period currently. Her last book, Britain after Rome, is one of the best recent works on the period. Guy Halsall's Worlds of Arthur is also excellent, and explains the limits of the evidence for this period especially well.

Elsewhere in the Western empire, changes were slow. Clovis - the first orthodox Christian king of the Franks - also considered himself (our sources say) to be a Roman. Given what we know of ethnic identities in late antiquity, this dual identity is not a contradiction. The Ostrogothic kingdom in Italy seems to have been genuinely upset when Justinian suggested they weren't legitimate successors to Rome's legacy in the sixth century. Culturally, many aspects of Roman life continue in the west for centuries. Change on-the-ground was a drawn out process, which started in some ways as early as the third century, was stalled with an aggressive new Roman bureaucracy in the late third and fourth centuries, accelerated with rapid changes in the fifth century, and wasn't completed for a long time after that.

Britain's a special case, because it was always on the fringes, and the evidence is particularly sparse and difficult to interpret.

What I'm about to say is heavily debated so be careful.

For a start how do we define Roman administration? if we define it was direct rule from Rome then Roman control had been slipping for a while, the 3rd century AD the empire was rocked by continuous rebellions as at one point (270's) splitting into 3 different empires with Britain and France under its own emperor. Though Diocletian was able to join it all back together again. All this suggests than control from Rome had been weak for a while, instead relying on economic and political influence to retain control. It is known that they had been withdrawing troops from Britain since 383 so its likely was becoming less and less important.

Also the events of 410 AD wasn't really a withdraw more a local uprising. After the sack of Rome the western empire had collapsed leaving a rump empire based around Italy with the rest going to the local rulers. Constantine the 3rd set himself up as emperor in Britain and started invading France to try and get to Rome. Eventually the British got so feed up of all this they drove Constantine's people out and set themselves up independently.

From here it gets complicated as few records survive, it appears that the British tried to keep the old ways going though we don't know how successful they were as the economic links of the old Roman empire broke down so far from the Mediterranean. Eventually this and the invasion of the Anglo-Saxons (some time between 410 and 731) destroyed what was left of Post-Roman Britain.

The Roman Field Army left Britain in 410, and never returned. However, the rump of the Roman administration remained, hence references to "Ambrosius" in slightly later works. Salway in "The Oxford History of Roman Britain" suggests that there had been a pattern of local Emperors in Britain, like Carausius and Allectus, so Constantine III was nothing new. Salway also suggests that the collapse of Roman culture in Britain was fairly absolute over the next couple of generations. He argues that Britain was so dependent upon Rome that it's removal led to complete economic collapse in Britain, leading the very rapid decline in city life, and the fragmentation of society leading to the establishment of many local kingdoms, for want of a better word. The garrisons of the fortified places may have maintained a degree of cohesion for a generation or so, but would then, effectively become self supporting farmers/soldiers, rather like the Celtic farmer/warriors that preceded the Roman invasion, based around their fort, now their regional capital and the hall of their local king, quite possibly the descendant of the garrison commander. There was no invasion by the Saxons. There had been Angeln and Saxones settling in Britain for close to 200 years before 410, with Germanic units recorded on Hadrian's wall, as well as Sarmations at Ribchester. These people would have continued to thrive in Roman Britain, reinforced by migration from N.Germany and Denmark, helped by the de-populating plague of the 4th Century.