There are various claims about the origin, but the shown marks were not used by either Libertas (San Marino, Italy) or William Pottery (Bristol, England). In addition, the often claimed production period predates the introduction of the British Merchandise Act and trademark registrations, so it is nonsense.
Contributor Sharon Spencer mentioned that she also believes the shown marks are not producer marks, but customised brand/series marks applied by an importer/distributor who had these goods produced elsewhere. She also pointed out that the quality of the products had apparently deteriorated. While the "PRUSSIA" marked items were still relatively OK, the "ENGLAND" marked versions had already deteriorated slightly, with the "REGISTERED IN" versions being the worst (e.g. the process used to create the flow blue effect had been taken too far).

M210933a
Circle with eagle head, "LIBERTAS" and "ENGLAND".
(Picture: Sharon Spencer)

M210933b
Circle with eagle head, "LIBERTAS" and "ENGLAND" plus "TRADE MARK REGISTERED IN U.S. AMERICA & CANADA".
(Picture: Sharon Spencer)

M210933c
Circle with eagle head, "LIBERTAS" and "PRUSSIA".