Right now I am thinking of doing a list of all chess sets - if that task weren't absolutely impossible to achieve *g*
Like this one: Somerset Collectables do no longer exist.
The only hint is the name "Tolkien Enterprises" which would give you a date prior to the name change in 2010 but that is all I know. Yes, I can't find anything on the net so this would also suggest pre-internet or early internet days (everything up to 2005, more or less, I'd guess.)
But except for that?
Yes, the top one should be a Bakshi-inspired one - at least the King looks like Aragorn, the Knight like film Bilbo, and the Bishop like Fangorn. But the one below?
I think both sets are Fairweather design, from 1988, commonly marketed by SIAB/Mascott, hand painted or not, as this set. They still come up on ebay. The bottom set is also Fairweather design, later marketed by Mascott Direct 1994. This set has a finer patina on Sauron's side than the Mascott sets. It maybe Somerset had an earlier "exclusive" license with Tolkien E.