I can offer some information on the Viking invasions, and maybe a little on the other periods you mentioned.

The Viking invasions and aggression in Britain culminating in the major events outlined in the show The Last Kingdom are long in formation. Although events came to a head in the last quarter of the ninth century, the Anglo Saxon Chronicle dates the first Viking attack to c. 787, and the more significant sack of Lindisfarne to 793-794. With such a long timeframe, the Viking attacks really straddle a transition from a Middle Anglo-Saxon period to a Late Anglo-Saxon period.

Looking at the beginning of this, the tail end of the eighth century, the political landscape of England is dominated in chief by Mercia. Wessex retains its independence, as does Northumbria and intermittently Kent, but both Wessex and Northumbria were plagued by short reigns and internal feuding for much of the eighth century, leaving Mercia probably the most powerful force in Britain. However, a "Mercian Identity" does not seem to be nearly as pervasive. The Tribal Hidage, a document thought to be produced in Mercia and listing it's client kingdoms and provinces, makes numerous distinctions, and lists some regions that otherwise have little historical footprint. The Hidage sets apart "the area first called Mercia" even from areas such as Hwicce and Hereford, which had long been part of a Mercian hegemony. This points to a more localised identity, centred around smaller polities that may at various times form a broader hegemony, but retain some sense of this local root. Archaeology and charters align to confirm a sense of borders between these areas. Cemetery excavation has uncovered a series of what has been dubbed deviant burials, or execution cemeteries (although how much this is an extrapolation from spotty evidence needs further research). Whether executed on site or not, these cemeteries contain burials of people varying from being tied hand and foot, to signs of post mortem impalation (the quintessential head on a stake perhaps?), to evidence pointing towards burying people alive. These cemeteries, in addition to being deviant from typical, Christian Anglo-Saxon burial grounds, are away from population centres, and instead placed what often became parish or hundredal borders. Whether these buried people were heretics, criminals, or some other reasoning, their siting along the edges of regions points towards not only an enforced local jurisdiction, but more importantly for your question a distinct idea of where an area is, and what is outside it. Beyond the later hundredal borders, some of these sites align with more contemporary charters, to say nothing of theories that some regions may date well into the Roman period (most compellingly in the case of the Worcester diocese, which has been argued to pre-date Anglo-Saxon conversion). With such a continuity and strengthening of ideas of distinct regions, these probably formed a great deal of people's identity.

What concepts of identity definitely was not in the late eighth century onwards well into the ninth century and really all the way until Athelstan and Edgar in the mid-tenth century, was English. The closest to English we get in the eighth century are a few charters from Mercia, naming Offa rex Anglorum, many of which have since been deemed spurious. Another tantalising charter wording is Sutangli (or Suthangli, or Australis Angli), i.e. South Angles, in several charters of king Æthelbald. These charters seem to be authentic, and hint at the possibility of a broader Southern identity (the logical border here being the Humber, delineating Northumbria and the more loose term Southumbria). However, this should not be taken too far in consideration of the above evidence, as well as subscriptions on these charters of figures such as Ulferth, variously described as a comes or a prefectus, either way indicating a subdivision of Mercia in accordance with what I've already discussed. These sweeping claims by Æthelbald and Offa seem more a political rhetoric, more in the vein of glorification than any sense of Englishness.

This is the scene that prevails when Viking attacks become a more pressing issue, towards the end of the ninth century. The Vikings conquer Northumbria and install a puppet, likewise with Mercia and East Anglia. King Alfred of Wessex is himself forced to go into hiding in a swamp for several years, and presumably during that time Wessex was without ruler or under some sort of Viking puppet state. The situation, put bluntly, was bleak. However, Alfred managed to assemble a force and emerge from the swamp, and after defeating Guthrum, Viking king of East Anglia, in 878, enjoyed about a decade of relative peace. However, in the early 890s the Vikings broke the peace, and resumed major raiding. This second date is significant, because it is concurrent with the emergence of two major texts for the period: Asser's Life of King Alfred, and the Anglo-Saxon Chronicle. Both of these are essentially major propaganda pieces for Alfred, essentially creating a narrative of a righteous king in a long slog against heathens, and of course eventually prevailing. A driving force behind them is an "us vs. them" sort of notion. The Anglo Saxon Chronicle describes citizens of London (not typically West Saxon) fighting alongside the king's thegns, or of Kentish ships fighting under Alfred's command. The Vikings, meanwhile, are invariably swept under the carpet terms of Danes or heathens. Clearly Wessex by this time had taken on substantially more territory than it's usual bounds; the Watling street border agreed by Guthrum and Alfred in 878 essentially divided England in two - Vikings and Wessex. However, this once again should not be taken to connote a sense of Englishness. As much as the Chronicle depicts a united non-Viking population fighting the Vikings, they are still distinguished as Londoners or the Kentish.

What Alfred did achieve, though, was the foundation for a more stable dynasty in England than ever before. From Alfred until Æthelred II, there is over a century of continuous rule not only from one family, but with a string of long reigns as well. This stability was coupled with the vast extension of Wessex in the coming decades. By the time of Edgar, all of England was at least nominally under his rule (law codes throughout this period denote a level of autonomy in the Danelaw, roughly East Anglia, much higher than elsewhere. There are also questions of the level of royal authority in Northumbria, with concurrent coinages running in the tenth century for a brief period despite Edgar's standardisation efforts). During this time, charters begin to regularly refer to the king as rex Anglorum, and with some force behind the words. It is telling that when Cnut conquers England in 1016, he conquers all of it, despite not campaigning throughout the entirety of England. This is a stark dichotomy from two hundred years earlier, when the death of a king generally marked the dissolution of conquered territories (for example, the aforementioned Mercian kings Æthelbald and Offa both held comparable amounts of land, but Offa re-subjugated, rather than inherited it). Clearly, the notion of English by the dawn of the eleventh century was radically different, and probably more unified, than it had been before.

I hope this at least spurs interest for further reading! I kinda got into a ramble, I'm not even sure if I answered the question anymore, and I've now got to go do my actual work :(. If this helps, I may be able to write a bit on other periods of English history tomorrow, but I'm equally sure more qualified people could deliver far better answers than I can.

TL;DR: To call the kingdom of Alfred "English" would be a gross overstatement. While it was the last independent major Anglo-Saxon power for much of the latter ninth century, it can be typified not so much by internal unity as by being not Viking. For centuries, Anglo-Saxon identity was defined on a much more local scale, and it wasn't until the tenth century and beyond that any semblance of Englishness began to emerge. Even then, internal dissent continued, with the usurping actions of House Godwine to name just one example. The notion of England, then, is a complex and convoluted one, and certainly one that cannot be seen in the ninth century.

Sources:

http://avalon.law.yale.edu/medieval/ang11.asp (Anglo Saxon Chronicle)

http://www.historyfiles.co.uk/FeaturesBritain/EnglandMerciaHidage01.htm (the tribal hidage)

Electronic Sawyer, S103, 108, 109, 94, and 101

Andrew Reynolds, Anglo Saxon Deviant Burial Customs

Steven Bassett, 'Churches in Worcester before and after the conversion of the Anglo Saxons,' Antiquaries Journal 69

James Campbell, The Anglo-Saxons

Dorothy Whitelock, English Historical Documents vol. 1 c. 500-1042 no.'s 32 and 34