Not sure why you should find hornbeam difficult to source if you are in the UK; it’s ubiquitous across the landscape and is not highly prized (goes to firewood mostly) so should be cheap as chips. However, you might consider investigating Robinia Pseudocaccia (Black Locust): grown for timber all over France and lots of UK importers currently.

I read once that cherry was used for watermill teeth. Apple has also been used traditionally. But I would have thought the main problem would be finding a wood that’s fine grained, hard and not too brittle, but that also remains durable in a wet environment. Hornbeam and sorbus are mechanically perfect but very susceptible to rot. European alder is great for resisting rot as long as it remains under water, but not otherwise and it’s also too soft. Elm was traditionally used for underwater structures such as lock gates on English canals; so I’m not too sure why it’s rated as non-durable here? One suggestion I would make is Robinia pseudoacacia (black locust in the USA), which is very hard and virtually never rots if it’s felled at the right time and moon cycle. I don’t think it’s very well known in England, but it France it’s extremely common, being planted commercially particularly for fence posts, so it shouldn’t be too expensive. Paradoxically a lot of the robinia fence posts for sale in France come from countries like Bulgaria, even though there’s so much grown here. You could even buy a couple of robinia fence posts and saw them up for your watermill teeth if they’re large enough.

I need it for the teeth on cogwheels, it has to be durable, shapable, resistant to water/rotting and liable to sheer if the mechanism jams. As we are not running the mill as it would been, the durability is less of an issue – maybe run it for a few hours a week not 18 hours a day.

then don’t use polyurethane, hornbeam oils up spectacularly well with a bit of danish. see my facebook page for a set or skittles i made in hornbeam. https://www.facebook.com/steveswoodenskittles/?ref=hl