I was in a touring production of this play. They used a scrim for all of the backdrops other than the professor's house. The actual sets were fairly simple but really effective. My favorite pieces were the wardrobe and the witches sleigh. The wardrobe would spin around. On one side it was a plain wooden wardrobe, on the other side it was white with fantasy/snowy designs. It also made it easy to use b/c you go back and forth from house to Narnia quite a few times in the beginning, and the wardrobe didn't have to be changed, just spun around. We also had these giant trees made out of painter's tarps (over a frame). They sprayed them silver and then put tinsel and glitter on them (sounds like a kindergarten craft I know), but they worked perfectly because they used lighting to change from cold to warm Narnia and all the "sparkles" on the tree picked up the colors of the lights. So in cold Narnia they were silvery/blue/white and in Warm Narnia they were really sparkly green.
Other than that, we had a huge beaver's dam, Tumnus' house which was on a platform and would roll out while he and Lucy were walking to his house, the pavilion, and the stone table. Oh wait we had an interesting witch's throne too. The seat was built between 2 giant white square columns set at an angle. The columns were covered by a type of white plastic that was translucent. There were lights in the columns which made them look more like pillars of light than columns. Message me if you would like pictures, and I'll try to find some.