Neglected seems wrong to me if the point is actually that it's native grass that's just naturally sparse. The word neglected usually implies being overgrown with weeds, brush, or invasive species, which seems to me like the opposite of bare or sparsely covered. So I would agree that it sounds wrong on the face of it.
Sward is surely archaic; another reason not to trust everything you find on dict.cc.
Lean turf is unfamiliar and looks suspiciously Denglish to me; I think of turf as by definition good grass, like on golf courses, and the word lean is not normally used for land. But who knows, it could be BE or something.
Unimproved sounds to me like it doesn't have infrastructure, that is, electricity and sewer lines and paved roads.
Nutrient-poor might be the best literal translation among the options we've seen so far, but I'm not sure if that's meant to describe its natural state, or if it's the result of something like overgrazing or overplanting, in which case we might just call it overgrazed grassland/pasture.
I don't think calcareous would be familiar to many people except geologists or soil scientists, but alkaline would be understandable, as would simply poor soil, or thin, rocky topsoil with a lot of limestone not far under the surface, which is what I picture when you mention Wales or Scotland. That is, is it possible that what's nutrient-poor is the soil, in the first instance, and only secondarily the grass? I wonder if that's partly why no literal translations are showing up.
If you need to keep it more literal, though, I would be inclined to go for something like sparse native grasslands, but that's just a description.