Thank you for the replies thus far. Mine is an unbranded (I think - I can’t see any markings indicating brand) hexagonal style reel indicated in the photos from bulldog above. It does appear to screw only in the CW direction but as I say even if I remove the handle and screw the two pieces together away from the reel body, they don’t stay together if you give a very gentle pull. They simply fall back apart. The exception to this is if I remove the small rubber washer. In that instance, it does seem to get purchase. That said, if I do then reinsert the arm without the washer into the reel body and screw, the same original result occurs; the two pieces do not remain joined.
I had considered perhaps some plumbers tape around the screw to see if that helped the two pieces link, but haven’t tried that yet as I didn’t want to cause any damage.