You wont find Rice spares for these. There wasn't many made and they weren't stocked routinely. But its not difficult to get some made up. Google for a supplier near you, give them the measurements and weight limit you want and they will make them up. They should come with hubs, backplates and brakes attached. You will then need to attach a brake cable as I think the Badminton used a rod. Its an easy job but a trailer mechanic will do it if you cant or dont want to.
I'd factor in it being expensive though. I think the axles on these were 1750kgs each which arent going to be cheap. Depending what you want the trailer for you might be able to downrate the axles and save some money. The box and frame isn't particularly heavy on these, about 1200kgs from memory but it was designed to take 3 horses, so had a 3500kgs weight limit. If this is for conversion you wont need anywhere near that capability