After a bit of research (googling) I have found that the correct name for my Tartle is actually
a pastry tamper
although I think Tartle sounds much better.
Veggie Gnome and Joolz thought that my object was a darning mushroom or similar, Ramsey thought it might have been something to wind thread or yarn onto, Jenny knew what it was but declined to say, (but then Jenny was the person that gave it to me), Liz J thought it may have been used to crushing herbs (and yes, Liz, it is lovely and smooth to hold) and Aunt 'Reen and Sandra had no idea.
Mine was a gift from my sister Jenny in New Zealand, who seems to have a knack for finding useful and attractive gifts. I don’t know if this exact style of Tartle is still available, the woodturning business (Pascal Woodturning, Ashhurst) where this one was made is still listed in the yellow pages. I did see a similar wooden one in a kitchen shop somewhere in Auckland last Christmas, but it didn’t appear to be very well turned, it had quite rough edges as if it needed a good sanding.
I had a quick look around my house and found two objects that would do the trick (they are the same size as the small end of the Tartle),
…. a film canister (not sure if you can still get these, I have a couple as they are quite handy for storing small objects)
….. and a champagne cork, (the film canister is probably more hygienic)
I haven’t looked for a substitute for the larger end yet, but I’m sure I could find something that would work.