I've been doing a lot of thinking about the early medieval period for a low fantasy book I want to write, including research into the use of horses by Anglo Saxon and Viking armies. Horses were frequently used, but apparently those who could afford them usually dismounted and fought in a shield wall with their men. Yet later, Heavy Cavalry would come to dominate the battlefield, with similar armor and weapon technology (mail, spears) existing. What change in Cavalry tactics and technology that made them a more effective fighting force than the English shield wall during that time?
edit: https://www.reddit.com/r/history/comments/g8l8yy/why_didnt_heavy_cavalry_dominate_in_premedieval/ I found this answer, which doesn't quiet answer the question. It states that medieval armies were decentralized levies, not professional enough to repulse heavy cavalry, which perfectly describes the armies of late 800s Britain! They were incredibly decentralized relying in the fyrd system which is essentially a levy, so why was Heavy Cavalry not used to defeat these armies?
It's disputed, both on the facts and on the analysis, but there is a theory that the deciding event here was the introduction to England of the stirrup.
The dispute on the facts is about just when Stirrups came to England. We can trace the spread of stirrups in Europe more or less from Southeast to Northwest, and it was taking place in the 8th and 9th centuries exactly the time you are asking about, and of course England would be just about the last place it would reach by that progression. There is some evidence to the effect that it was earlier in this period some competing evidence to the effect that it was later, but just about everyone agrees the technology had not been widely adopted for use in mounted combat in England by the late 800s.
The dispute on the analysis is not really specific to England but it concerns just how good or bad heavy cavalry would be if they did not have any stirrups. Could you have a heavily-armored mounted Warrior if he didn't have anywhere to put his feet? After all, Parthian Cataphracts start showing up in the record around 300 BC, without a single stirrup among them, and they were a highly effective military force for a long time (for what it's worth, they did sort of tie themselves into the saddle with leather clamps to prevent themselves falling off while fighting).
But without trying to be definitive, it is perfectly possible that even if a well-to-do fighter who could afford a horse had seen or heard of stirrups, and even if he thought they were just dandy for riding around between towns or battles, he might not trust them for serious combat work if all his experience involved standing on the ground to fight.
ETA sources: On the advent of stirrups in Britain: Seaby, Wilfred A. and Woodfield, Paul (1980). "Viking Stirrups from England and their Background". Medieval Archeology, Volume 24: 90.
For two opposing views on whether or not stirrups were essential to mounted shock warfare, see: Medieval Technology and Social Change, Author Lynn Townsend White, Publisher, Oxford University Press, 1964, ISBN 0195002660, 9780195002669
D. A. Bullough, English Historical Review (1970) and Bernard S. Bachrach, "Charles Martel, Mounted Shock Combat, the Stirrup, and Feudalism" in Studies in Medieval and Renaissance History (1970).
/u/Silas_of_the_Lambs has already mentioned the importance of the stirrup so I wanted to chime in about the importance of the shield wall. The late-C9th fyrd wasn't just a bunch of farmers handed a sharp stick and pointed at the nearest Dane, it was a (usually) well-disciplined fighting force drawn from myriad small warbands. The Fyrd faced heavy cavalry on a number of occasions and, well, it won. After all, the strength of medieval heavy cavalry isn't in its charge - although that is undoubtedly useful - but in its tactical and strategic flexibility. You can see the utility of heavy cavalry in two battles: Lechfeld in 954 and Alnwick in 1174. At Lechfeld, the newly-established milites of Otto I turned the tide against the Magyars as their speed and manoeuvring disrupted their light cavalry skirmish tactics and forced them into a battle for which they were under equipped. At Alnwick in 1174, the strategic flexibility of English heavy cavalry allowed for the garrisons of Newcastle, Prudhoe and other castles to rapidly combine and achieve local numerical superiority over part of the Scottish army laying siege to Alnwick, capturing William the Lion before his army could effectively respond.
So let's look at a prominent example of knights fighting a shield wall: the Battle of Hastings in 1066. "But wait", you might say, "the Normans won at Hastings!" And you'd be right, but the Norman victory didn't come from the strength of a cavalry charge - indeed the Normans spent the best part of a day charging the English shield wall to very little effect. Even Norman sources such as Guy of Amiens Carmen de Hastingæ Proelio admit that the English shieldwall successfully repulsed Norman cavalry charges throughout most of the battle. Where cavalry turns the battle is in its ability to manoeuvre and respond rapidly: when a flank of the English line breaks ranks to charge downhill in pursuit of withdrawing Norman knights, Norman cavalry is able to quickly counter-attack and catch the English out of formation, where they're far more vulnerable. Almost a century later, Richard of Hexham's account of the Battle of the Standard similarly depicts an English shield wall standing firm in the face of a Scottish charge.
It's also worth noting that in the 890s, a Danish force which invaded England did so via France, where it purportedly defeated a Frankish army and 'became a mounted force'. However, that force was still defeated by Alfred's army outside Rochester.