But, crucially, RN badges seem to all be surrounded by a rope pattern design
@AnonyJ - your logic is impeccable (and I had meant to comment upon this earlier).
Another close-but-not-quite match is this famous badge:
Now: here is some partially-informed conjecture on my part....the rope surrounding naval ship badges can indeed either be round or sharply-straight.
I had always lazily-believed this to perhaps be linked in some way to the differences (now largely historic) in British naval officer uniform rank-braid, worn in gold thread near the cuff or on the shoulder.
This is presented in an increasing quantity of 'rings', such that eg a Commander wears three, and a Captain wears four: very similar to the derivative rank arrangements worn by the RAF, many other of the world's air forces, and also of course civil aviation.
But military nautical forces have varied their 'rank rings', to the extent that naval formations such as the old Royal Naval Volunteer Reserve was known as the "wavy navy", because it's braid (including importantly, the top "executive curl" which is a simple circular ring for regular Royal Navy and now the active Royal Naval Reserve) became replaced by various geometric rope-like shape combinations, for different hierarchies of non-regular/part-time military seafarers in the Commonwealth's navies.
Aha...I've had a possible Eureka moment: I shall post this, and return here when I can....
EDIT....hmm, yes, just as I suddenly remembered. The different rank-braid badges originally worn by 'Wrens' (or, more correctly, officers in the WRNS, W
omens' Royal Naval Service, and their Commonwealth fellow equivalents)...for their 'executive curl' or top-knot:
Which is therefore making me wonder: the badge could be to mark female military nautical Service on board something like HMCS or HMAS Edinburgh? (nb I have no idea if these ships ever existed under under Canadian or Australian flags) If so, it might be some form of military naval 'sweetheart' badge (a military-themed badge, sometimes created from multiple source elements on an unofficial basis, worn by associated Civilians and veterans, to mark Service or affiliation)