I'm certainly not an expert on WW1 badges and that's why I suggested that you do your own research. I'm 'pretty sure' that some WW1 officer's badges (which were a different material) had the revolving wheel...It would 'seem' that during this period there were also 'Other Ranks' badges which featured it too, although officially there is no record. There were dozens of suppliers of badges and plenty of troops looking for replacement or duplicate badges for their 'best' uniforms....and this would have continued in the inter-war period....In an army whose officers had to purchase all their own kit, the idea of 'private purchase is not strange. I'm not saying it is, or it isn't any of these but it differs from the norm so if you want to collect this sort of thing, you either have to accept it as 'good enough' for what you want, or take your research a step further which probably means buying books.
You could also try asking about the medals here: British Medals Forum • Index page And badges here: The British Military Badge Forum
Utku Might be worth doing some research and a good starting point is here Orders, Decorations, Medals and Militaria (17 March 2021) Lots | Dix Noonan Webb it will also provide you with guide prices TD