This one really intrigued me for some reason.
Your post was very helpful as I thought the "horizontal metal bar" was a slot for a flathead screwdriver, but I was clearly wrong.
I'm pretty sure this is indeed an umbrella tip (as Taz42o suggested earlier) because of a description of an item in the collection of a British museum:
"Umbrella, with small ivory handles, a pressed metal collar, decorated and stamped with a crown and legend 'Best Improved.' With a metal ferrule and cloth cover."
Sadly there isn't a photo, here is the link:
Search Results - Hull Museums Collections