Rare-earth minerals like synchysite and xenotime are widespread in small veins cutting brittle lithologies (e.g. ashflow tuffs, dolerite sills and dykes) in the slate-belt of North Wales, but generally the quantities are academic!
Nodules of monazite - a rare-earth phosphate - are common in certain Ordovician sedimentary rocks in Wales, and are concentrated in the rivers draining such areas, but again this represents a pretty low-grade resource.
Cheers - John