Why didn't I think of this??!!
At my new school, whenever students have a quiz or test they use quiz shields. Basically they can be made from large pieces of card concertina-ed to prevent wandering eyes between students. Once you have made a set, just store them in the cupboard for next time!
This is really good if you are in a room with permanent desks (science lab) or a small room where moving desks is difficult (not to mention time consuming!).