Hello
Your 'naval' button photo is slightly blurred and I can't quite make out the letters. The last two appear to be 'YC' in gothic script - is there any chance the first two letters are 'RM'? In which case it may well be the Royal Mersey Yacht Club.
Your two monogrammed buttons are not British military and I would suggest that they are most likely 'company' buttons - bus or tram corporation, business company, that sort of thing, where they just used their initials as a device on buttons and badges.
Roger
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