Looking at Google I found a recipe for home made sugar free mints. They were made with Xylitol which is easily found in the supermarkets.
The recipe appeared very simple: double the amount of xylitol to water and heat to the "hard crack" stage before adding peppermint oil before pouring spoonfuls to cool. .
However, when we tried it, all that happened was the Xylitol mixture just got hotter and hotter till it started to discolour. Even when it reached the point at which my thermometer couldn't go any higher (200C !) it hadn't reached a soft ball stage let alone a a soft crack. It didn't actually caramelize or taste burnt.)
During cooling the mixture eventually solidified and crystallised to form a a sweet with the texture of Kendal Mint Cake rather than that of a boiled sweet and did actually taste quite nice.
Xylitol is extremely poisonous for cats and dogs so please do not feed to them.
The Xylitol syrup will be very hot so please watch the pan all the time while it is heating and be very careful when handling it.
After this first attempt I did some more googling and found another, more helpful, item about working with xylitol written in a more scientific manner.
This just suggested adding no water but heating the Xylitol by itself till it was molten at about 106C and then pouring in a block to solidify and crystallise. This again left something more akin to Kendal Mint Cake.
The results can be seen in the photo below
the picture below is the crystal (someone suggested it looks likes cod fillet)
it is amazing what a bit of photo dressing can do!
The coolness of Xylitol and the peppermint oil made for a great tasting sweets but the texture was not what I was expecting.