I meant that many riders when they feel their balance is compromised will curl forward and maybe even grab at the mane or pommel of the saddle. That curling up is the "fetal" position. It is very instinctive for humans to take this posture when we feel scared.
I just assumed it might have been part of your experience when first riding in the itsy-bitsy English saddle.
I know that when I ride bareback, and it's pretty rare these day (too old, I am), I will have to counteract my instinctive urge to collapse forward and cling to the horse if I feel compramised. Staying upright and centered over the horse keeps me the safest, but my instincts sometimes go the other direction.
When you take your next lesson, keep that thought of riding "inside " the horse, just a few inches. As you go around and lose your balance, 'cause you KNOW it's going to happen, you just recover your balance and go immediately back into what you were doing. Just blow if off with a deep, exhale and go on. Don't allow your mind to wander in the area of "what if . . .". You need to get immediately back to the present and back to your centered feeling. After time and lessons, the amount of time you spend feeling unbalanced will lessen and the time centered will grow until it long outweighs the other . Been there, done that.