So there are not specific battles that are recorded with such a battle plan, simplistic as it is, and for those of you who have not seen the show, the process is spelled very clearly for the audience. The Northumbrian army splits into two, one reserve force and one attacking. The attackers break ranks and slam into the viking shield wall and try to physically force their way to break the shield wall, very reminiscent of the idea of othismos as I understand it. Seeing this progress, the reserve force joins the fray and as soon as they engage, a hidden force of vikings emerges from the trees, surrounding the Northumbrians and cuts them down. Many of our sources that deal with battle and wars, The Battle of Maldon the digressions of Beowuf, don't actually give significant detail on the process of battles, so it is very hard to say such a strategy was never employed in warfare in Anglo-Saxon England, but we have some additional information on how these battles would have actually progressed. There are certainly aspects in this battle that are correct. The focus on the shield wall as a relatively immobile fortress, the division of an army into a few different moving parts, and the close quarters fight of infantry as the deciding factor of the battle do check out but there are a number of omissions (and this is not to touch on the disgraceful rendition of armor and weapons*

Let's back up for just a moment though

In the 9th century warfare in England was changing rather rapidly. The scale of viking raids, which started very small in the late 790's, had grown to incorporate a micel here, or great army, that had landed in England and was operating across the island, and occasionally dipping into Francia. The Anglo-Saxon kingdoms of England were in various states of disarray against the interlopers. Northumbria was in the middle of a civil war when the army showed up, East Anglia was overrun and its king martyred, but Mercia and Wessex were able to stand firm (with some set backs) and eventually unite, drive the Norse back, and unite the island. What did this process look like on the ground though? The systems of warfare that had predominated in the heptarchy (the period of England's division into seven different kingdoms, ending shortly before the Norse incursions) was inadequate. This largely revolved around noble figures and their retainers being called up for war. However this process was slow, it took time for all the various hangers on to local notables to muster to fight, and it was a poor match for the Norse.

The great advantage of the micel here was its mobility, not only through the famed Norse longships which could sail up rivers and around the North Sea with (at the time) impunity, but our sources also indicate that the Danes were able to acquire horses in East Anglia to further aid their military campaign. Now we need to be clear through that the scale of this attack was still rather small, even by medieval standards. The size of this "great army" was certainly no more than a few thousand, and that is at the upper range of estimates, but its mobility, the division of Anglo-Saxon England, and the sluggish ability of Saxon forces to rally against them made it very difficult for the remaining A-S kingdoms to effectively counter the Norse raiders. Indeed the mobility of Norse forces to seize fortified settlements before a response could be effectively mustered meant that A-S armies were often forced to waste long stretches of the campaigning season running around trying to besiege the newest seized fortress and force a confrontation that the Danes were happy to avoid.

Indeed the decisive battles between two armies that so capture the imagination were quite rare in this time period. The Norse wanted to avoid pitched battles as much as possible, the Saxons likewise often saw no reason to force battles when sieges and bribery were usually enough to see the Danes off. But battles nonetheless did happen. When this did occur there is enough evidence from surviving sources, both literary and visual, to give a rough, and I must emphasize rough, outline.

Both armies would draw up into whatever advantageous positions they could, trying to use high ground, rivers, choke points, woods, etc... to their advantage. Christian armies at the time often would hold prayers, fast, or engage in other religious practices before the battle stared. The battle would begin usually with an exchange of missile fire (some sources indicate the presence of negotiations before a battle between the two sides, though this may be a literary flourish or a more ad hoc basis). This could be arrows, spears, slings, etc... and this served to attempt to soften the other shield wall before melee combat was joined. The sides would then clash in shield wall formations to try and break through the opposite's formation. Cavalry may have been present in limited numbers, though my interpretation of the available evidence suggests that cavalry were fielded quite rarely as a dedicated force. (Guy Halsall disagrees in Warfare and the Barbarian West and makes a solid case for the presence of cavalry at at least some battles in this time). Often cavalry is only mentioned in cases of ambushes or pursuits suggesting that their role in deciding the battle was limited. Instead the focus came down to which side broke first from melee. When a shield wall broke down the people within it became exceedingly vulnerable and most casualties came only after the formation collapsed. (This is also what happened in the Battle of Hastings in 1066, the Saxon shield wall held strong and only after the Saxons broke ranks to chase down the Normans were they dispersed enough to finally allow the Norman cavalry to decide the battle)

This would occur through what is often termed in poetry of the time "the clash of spears", though certainly other weapons were used as well. There might well be lulls between the fighting as each side regrouped and collected for another push, but eventually one side would break and decide the battle, this could take place because of mounting casualties, the death of the leader of an army, or the flight of others from the field. The Battle of Maldon (a fictionalized retelling of events that happened in the 10th century) turns into an English rout when many of the English break and run after their leader dies, the remainder of his forces of course choose to fight to the death to stay by their lord.

Now this may give you the impression that the shield wall was more or less invulnerable in certain situations, especially with the high ground and with numeric superiority, but there are cases, the Battle of Ashdown for example (as well as Hastings) where aggression was able to break the shield wall, and defensive positions, relatively easily. There are several examples of both the Saxons and Danes splitting their forces into multiple parts in battle as well, and while the actual functioning of these divisions is unclear, we should not imagine one single line of shields with no tactical subdivisions that could be wielded independently.

So to return to the original example of The Last Kingdom while there is no direct evidence of such tactics being employed, and there are omissions (the lack of missile warfare, the rapidity of the battle, as well as the lack of coordination on the Northumbrian side), there are certainly accurate aspects that do bear witness to 9th century warfare.