So I'm trying to come up with examples of specific technologies that would have been lost in the outer regions of the Western Roman Empire and (especially) Britain between say, 300-500 AD.
Ideally, I'm looking for things that have fairly obvious applications. Not esoteric knowledge, but the kind of thing that would have a direct impact on the lives of people living at the time. One example would be, say, the ability to construct a major aqueduct for a city. The difference between the city with and the city without would be huge and immediately obvious.
Maybe another way to phrase the question is: if a fifth or sixth century British town could magically resurrect one or two (non-military) Roman technologies, what sorts of things would have the biggest impact on the welfare of its people and do the most to stem the de-urbanization that was going on at that time?
Thank you!
Bricks. Now in fairness roman bricks were rather different from modern bricks being effectively thick tiles but brits aparently stopped making them.
Lost is always slightly questionable due to the difference between not knowing how to make something even in theory and lack of reason to do so.
Coins are a slightly tricky case. Coins stopped being minted in britian but the current argument appears to be that old Roman coins and a few contemporary coins continued to circulate on at least a limited scale (Early Anglo-Saxon Coins pages 12-13 Gareth Williams)
If we accept Foss Dyke as roman (canal nerds I know think it is) then canals. Good quality roads also declined.
I would recommend you read Bryan Ward-Perkins's "The Fall of Rome and the end of Civilization". He might be a bit drastic in his conclusions, but he draws a very good picture of the decline in material goods in the early middle ages.
Pottery is one example. In Britain, the quality and quantity of pottery declined drastically. The potter's wheel fell completely out of use, and the pots were more fragile than before due to insufficient frying.
Roman building crafts also all but disappeared. There is no evidence of continued stone quarrying or building, or manufacturing of mortar, bricks and roof tiles.
Anglo Saxon elite craftsmanship had its strenghts, as any google image search will tell you. However, as Ward-Perkins puts it: "What had totally disappeared, however, were the good-quality, low-value items, made in bulk, and available so widely in the Roman period". Maybe not very relevant to you specific question, but I thought I might add it just for fun.
The Hypocaust, otherwise known today as central heating. A central furnace ,which was regularly heated by slaves, would release hot air amongst spaces in the the walls and under the floorboards, heating the house. Hypocaust' fell into disuse after the fall of the Roman empire.