There were no "Western Group" coins as such. The "Western Group" as far as "British Caribbean" would have been concerned would I presume be Jamaica, Bahamas, Turks & Caicos, Cayman Islands and perhaps British Honduras/Belize.
At the time this coin was made, Jamaica and British Honduras were making their own coins. Other "Western" territories would have either used British currency or coins from the other territories.
British colonial practice at the time was to "group" nearby colonies and territories together into monetary unions, rather than having each colony making it's own coinage. Thus, "British Caribbean Territories" instead of coins for each tiny little island-colony; "British West Africa" and "East Africa" instead of coins for each colony in Africa, and so forth. Only the larger and/or more isolated colonies made their own coinage.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis