The brewery it came from sold up to Truman's in 1958, so it's older than I am.
It's actually a screw cap with a rather wide thread on it:
It was in the neck of the bottle when it was found, and fits it surprisingly snugly. Unfortunately, the neck of the bottle wasn't attached to the rest of the bottle.
According to my wife's subsequent research, it's an ebonite screw beer bottle top, which fell out of use in the 1930s. That would make it something like 80 years old.
It's sellable on eBay for all of 99p.