The Anglo-Saxons were perfectly capable of Roman building if they required it: look at the Anglo-Saxon period remains at churches like Brixworth, Northamptonshire or Deerhurst, Gloucestershire to see standing examples. They could also maintain Roman architecture: the remains of Roman walls in Lincoln and Leicester survive because they became part of Anglo-Saxon defensive circuits. So generally not choosing to build in a Roman style was a choice.

One thing to get clear though is that wood and thatch is not inferior as building materials to stone. People in England still have thatched roofs because they work as well as tiles at keeping out water; it was historically also often easier to find the reeds required than to bake clay tiles (or quarry slate ones). And wood is also waterproof and retains heat inside a building - otherwise the tradition of timber building in Scandinavia makes no sense. So the image of people huddling under leaky thatch you present is unlikely unless the building was derelict.

Another thing to remember is that the Romans did not build exclusively in stone. Whilst stone remains are more notable and have generally been prioritised by archaeologists until the last couple of generations, no-one has ever suggested that everyday housing was of stone. Whilst a high-status villa was likely to be partially stone, it's likely that lower-status sections were built of wood; whilst we tend to think of the Roman army as builders in stone, we need to remember that half of Hadrian's Wall was built of turf and that buildings within forts were normally wooden constructions. The normal inhabitant of Roman Britain certainly didn't live in a stone house made of regular blocks mortared together. Rather a fine stone building was a mark of someone's status within Roman society, showing they had the power to construct something in the style associated with Rome (and as inscriptions recording the person/military unit who built things show, this was an act of displaying that power). To build a stone theatre or a stone villa in the Roman style was a way for someone to declare their success in the Roman system.

So for an Anglo-Saxon, who was not trying to be a successful Roman, there was no status to be gained from building in stone when wood would do and is generally a lot easier to obtain. Hence high-status halls around the seventh century were wooden, but still large and impressive structures. It's notable that when Christianity was adopted, something that was very much Roman in an Anglo-Saxon context, churches were built in the Roman style (although many early churches were likely originally wooden), once more as a symbol of status: the early-eighth century Life of Wilfred by Stephen of Ripon for example focuses on churches built by its protagonist as a sign of his status and virtue.

Building Roman-style buildings was not a case of building better buildings (why would an architectural style developed around Italy work well for Britain?). It was a stylistic choice and expression of power within a discourse where being Roman was high-status (being provincial was a low-status thing to Romans). For the Anglo-Saxons, who were defined by not being Romans, building in stone in the Roman style was not a form of status so they did not do construct in this way. Instead they used other building methods that were at least as good for providing warm shelters.