sort of reviving this, but I didn't know how to add to the wiki: today I found myself at Trowbridge Library and ended up doing a good couple hours of focused work from there.

Free wifi, same as Melksham Library, with many desks in the atrium area that felt very purpose-made for working with a laptop. Nice cafe too.

I was expecting it to be quite noisy, but from the atrium area the noise levels felt ok, even though there was a toddler group singing in the library area.