We can safely assume that Thames was a retailer and distributor in the 1960s, rather than a producer, as the same items can be found with markings or stickers from other companies. For example, Thames item #3640 is identical to Arnart item #3640.
One noteworthy feature is the use of the term "BONE CHINA FLOWER" on some items. I wonder if this is somehow linked to items marked "BONE CHINA LACE" ?

M220810a
Sticker reading "THAMES" and "HAND-PAINTED" together with "MADE IN JAPAN".

M220810b
Same sticker as before but with an additional on-item mark reading "BONE CHINA FLOWER".