Definitely not the most common name for inland bodies of water by a country mile though. "Pond", "pool", and "lake" are more common.
So I did a quick search to check, both from memory and by looking at the map – not because I doubted you being right in general across the UK, but because locally 'mere' is so common.
Anyway, towns or bodies of water with 'Mere' in Cheshire: Mere, Mere Heath, Ellesmere Port, Blakemere, Delamere, Oakmere, Tatton Mere, Comber Mere, Pickmere, Manley Mere, Shakerly Mere, Marbury (means 'Fortified town by the lake'), Marbury Big Mere, the Quoisley Meres, Flaxmere, Hatchmere, Radnor Mere, Astbury Mere, Rossmere, Rostherne Mere, Nunsmere, The Mere, Little Mere… and then I got bored, so I may have missed a couple. Anyway, that's at least 23, and Cheshire is not a noticeably watery place, compared to some other counties.
In contrast, there are very few lakes: I could find Oulton Park Lake (man-made in the late 18th Century), and Acre Nook Lake, Lapwing Hall Lake, and another unnamed one – a series of quarry pits turned into a watersports centre in the 2010s.
So it looks like that in Cheshire at least, the normal name for a 'larger than a pond' body of water or nearby town is 'mere'.
Thanks for sending me down this interesting (well, to me, anyway) rabbit hole…
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.
I suspect there’s a Mercian link here somewhere…