Why didn't pre-Norman English kings build stone town walls?

in troubled areas.

This is slightly to miss the point that these were troubled areas because of the Normans. In modern times, consider the defensive perimeters around the Green Zone in Iraq, or around army camps in Helmand Province in Afghanistan. Regular family compounds have walls too, but on a very different scale because the level of risk is different.

In the Anglo-Saxon period, the purpose of town walls was primarily to defend the town's citizens against external aggressors, most notably Vikings. In the Norman period, the purpose of walls was primarily to defend the Normans against the people whose land they now occupied. The Normans are best known for building castles, not city walls.

many defensive city walls were built

And this is another misconception. The Normans built walls out of wood and earth. Even castles (the famous Norman motte-and-bailey design) were built out of wood.

A very, very few castles were originally built of stone, where they were at the highest risk. They represented a phenomenal investment in resources, and were correspondingly rare. See for example this link, and consider Edward I's architect's complaint with an expenditure of roughly £2000 annually, 200 years after the Norman Conquest:-

In case you should wonder where so much money could go in a week, we would have you know that we have needed – and shall continue to need 400 masons, both cutters and layers, together with 2,000 less skilled workmen, 100 carts, 60 wagons and 30 boats bringing stone and sea coal; 200 quarrymen; 30 smiths; and carpenters for putting in the joists and floor boards and other necessary jobs. All this takes no account of the garrison ... nor of purchases of material. Of which there will have to be a great quantity ... The men's pay has been and still is very much in arrears, and we are having the greatest difficulty in keeping them because they have simply nothing to live on.

And that's for a king in fairly-well-undisputed control of southern England and reasonable control over the rest of the country, and after the increases in agricultural productivity that the Normans brought in.

Was it a question of money?

Money and people, yes. You needed to hire enough stonemasons and labourers to make it happen, and this was never cheap.

Was it a question of skill?

This also is worth mentioning - not skill in construction, but in military imagination. The Saxons defended their towns, and they were all in it together. Once the town wall went down, that was it. But then you needed to invest enough to rebuild the whole town wall in stone, otherwise it was a waste of time. Some towns did, later, when they could afford it, and you got the prototypical curtain-wall design.

But the Saxons simply did not have the concept of a castle, or of defense in depth. The Normans did, and that gave them a two-stage defensive strategy where you could abandon the bailey if you were overrun and retreat to the more-strongly-built keep on the motte. At this point you have a defensive feature (the keep) which you can build fairly strongly and for not too much money.

And now you have the skills to do this, and when money allows, you can start building on that starting point. You often see with town walls that the keep defenses are extended with walls around the bailey, but leaving the houses outside the bailey less well defended; and then further walls are built beyond that; and so on. This is generally an process of progressive expansion as resources permit, not a top-down town planning exercise.

They did.

The Anglo-Saxons still used fortified areas and cities or towns, re-used old ones and build them anew.

It just takes a bit of time, effort and money to develop those walls and fortifications, to build and to maintain them. And perhaps a bit of an incentive. Like say, not Norman but simply Viking incursions, or earlier some extended 'local troubles'.

The central word to look for is 'burh', cognate to burg, burgh burough etc.

Though they nearly always started with ditches and palisades, or whatever was locally available. That is of course exactly the same for later Norman developments of fortifications.

One prime example would be Alfred the Great's capital Winchester, with it's wall remnants still standing:

The burhs were made in a variety of different ways, depending on materials available locally, and the size of the settlement or area it was intended to defend.

Frequently, a burh was built on the site of pre-existing fortifications. Sometimes, the Anglo-Saxons would simply repair old Roman walls in towns such as Winchester, Exeter, York, Burgh Castle, Portchester and Dover. At other times, they would build on the site of old Iron Age forts, such as Dover, utilising the old ditches and ramparts.

However, the Anglo-Saxons did not just use old fortifications. Many of the burhs built by the Saxons were entirely new fortified sites, built on strategic sites on the coast, near ports or overlooking roads and trade routes. Substantial new towns were built on flat land with a rectangular layout, at for example Oxford, Wallingford, Cricklade and Wareham.

Traditionally, burhs were constructed first with a massive series of banks fronted by a ditch. The bank was typically timber faced and timber revetted. This was topped by a wooden palisade of stakes, up to 10 feet (3.0 m) high, with a walkway. At towns such as Tamworth, the ramparts would decay and push outwards over time, meaning that the ditch and bank would deteriorate. To solve this, Anglo-Saxon builders faced banks with stone, thus further reinforcing the defences and improving their life span.

"The walled defence around a burh. Alfred's capital, Winchester. Saxon and medieval work on Roman foundations."

— WP: Burh

One important note may be here that it is not solely focused on defending one point, or one front-line, like Hadrian's Wall, but defending 'in-depth', controlling strategic points to cover the land with protection.

This is not to deny the important access rivers provided to inland regions, but it was in their use as a vector of entry to the overland road network that they were most significant in a military context. Travel along rivers did not automatically permit the pillaging of estate centres—in many places, a river such as the Thames is surrounded on one or both sides by a wide natural floodplain that probably consisted in the Anglo-Saxon period of heavy marshland. Disembarkation along these stretches of river would have been treacherous, and a ship-borne force would need to find appropriate places to come ashore—for example, established landing places or fords. Movement upstream could be slow and predictable from the viewpoint of defending forces. Roads, on the other hand, cut across important estates, regularly intersect with other roads, and allow more rapid movement by forces not excessively burdened with booty or equipment.

The fact that crossings were the priority of military planners can be seen from the location of strongholds throughout Wessex and especially along the Thames. The construction of forts at both ends of the same crossing simply provided a more reliable defence of that crossing and greater control of its use. The securing of major fords was important from both defensive and offensive perspectives. On the one hand, it allowed speedy and uninhibited movement of troops across Wessex and also, for campaigning purposes, into hostile territory; on the other, it denied enemy access to the same crossings into Wessex or easy movement within the kingdom.
— John Baker and Stuart Brookes: "Beyond the Burghal Hidage Anglo-Saxon Civil Defence in the Viking Age", History of Warfare 84, Brill: Leiden, Boston, 2013.

From that book, some illustrations:

Anglo-Saxon Malmesbury

Archaeological evidence from the 1968 excavations and imaginative reconstruction drawing of the Tamworth gatehouse.

The areas of burhs.

Models of warfare after Luttwak, showing A) Linear defence, B) Defence-in-Depth.

Map of beacons in Kent, by William Lambarde, “commissioned by Lord Cobham in order to have multiple copies made, as a guide to the effective use of beacons. The posi- tions of about fifty beacons are marked, with lines indicating the direction of the signals given off by them.” Originally published/produced in 1585.

20-mile radii drawn around the first-phase burhs of the Burghal Hidage.