Chestnut and Willow are the two that I've seen examples of, but I seem to remember there are other very useable species in the UK, such as Lime. I seem to remember there are a number of people offering courses in the skill, but I don't know details for those.
1. Google "Black Ash Baskets" to see what they look like.
2. There's a British(?) weaver building fantastic baskets for the species of ash that is native to the UK,
and it is not Fraxinus nigra, found in NE North America.
He's getting better and better with every basket that he posts in other websites.
Do not recall seeing him here in BCUK at all.