Many early Parker-Hale and BSA rifles were built on FN actions, but there were many also built on the same Yugoslavian-made actions used in the Mark X rifles.
The BSA Hunter was a Mauser like design, but as far as I know they built them themselves in the UK. If you can supply any more information about any BSAs built on FN or Zastava Mauser actions, I'd appreciate it.
Parker Hale OTOH, made up / commissioned / imported all kinds of things. I have a PH 30-06 that uses a Spanish Santa Barbara action that was sold in the US as a J.C. Penney, complete with a 4x J.C. Penney scope! Times were different then.