To take a different direction than what's already been suggested. I would look less into the blankets moving and more into you moving.
The less you move in your sleep, the less likely you are to displace the blankets. If you do displace the blankets then, it's going to be because you were getting too warm and threw them off; there's nothing to fix that except fixing the temperatures in the room.
Start training your body to move as little as possible. The easiest way to do this is by sleeping on a couch for a while. Unless you have a behemoth couch, there's not going to be enough room for you to toss about like if you were on a bed.
Another way to train your body to lie still, is to place two objects on either side of you in the bed. Two pillows usually work. When you start to roll in your sleep, you'll subconsciously recognize that there are the objects in your way, and keep from moving about so much.
Be warned though, that once you've done this, you can get stuck with it being difficult to sleep when you're not in a specific position that you've trained yourself to sleep.