This question is about defensive city walls, not longer walls such as the Great Wall of China or Hadrian's wall.
After the Norman conquest, many defensive city walls were built by Norman kings in troubled areas. But why did the pre-Norman kings not build these walls?
Did they think there was no need of such walls?
I disagree. We know that building or burhs was common during the period1. England certainly faced many domestic as well as international battles1. We know from the Anglo-Saxon Chronicle that Roman walls, that is stone walls originally built by Romans during their occupation of Britain, were of strategic value in battles. There is evidence that such walls were tended to and maintained by quite a few pre-Norman English kings (e.g., Alfred with the London walls and Æthelflæd with the Chester city walls [1, 3]).
Was it a question of money?
Robert Tombs1 writes that England was quite rich at the time. He does not cite or note how rich but he notes that Æthelred was able to raise £250,000 to pay off the Danish invaders. Edward the Confessor built Westminster Abbey in Romanesque style which would have cost a lot of money. He also writes that some Anglo-Saxon kings were richer than their European counterparts and even their later Norman successors. But besides these one off claims, do we know how rich pre-Norman English kingdoms were and how much such wall building would have cost at that time? Was the money spent elsewhere?
Was it a question of skill?
If it was not a question of money then was it a question of know-how? We know that stone defensive walls were being built on the European mainland and in the Eastern Roman (Byzantine) Empire well into the 10th century as a continuation of ancient Roman era practices2. England did have trade connections to the continent --English wool was sold in France and Italy and Byzantine pottery from the 6th century has been found in England. England also had diplomatic connections to various mainland kingdoms and also the Eastern Roman empire (Wessex records from Alfred's time record diplomatic visits both ways, Cnut attended Conrad II's coronation1, Edward the confessor sent ambassadors to Roman emperors etc.). So if the mainland Europeans and Byzantines knew how to build walls then surely such knowledge could have come to England.
Byzantine Ambassador: Agreed this is an internet source but it appears well cited.
The English and Byzantium: A Study of Their Role in the Byzantine Army in the Later Eleventh Century. This reference is mainly concerned with eleventh century but there are some references to earlier exchanges between Byzantium and England.