I don't know of a single "mere" in Scotland or Ireland. I doubt there are any in Wales... Maybe in the eastern bits that are less Welsh speaking. I'm surprised about Cheshire. Maybe it is more widespread than I thought it was! But it isn't a word I hear used in spoken in English outside of place names.

Some of it is regional. "Tarn" turns up in the Danelaw. "Lough" turns up in the far north of England for about twenty place names, which is a variant of "loch", but is pronounced "luff". You can find some "loughs" near Hadrian's Wall.