Full disclosure: I have not read all the responses.
Having said that, can your instructor put the horse on the lunge line and keep it moving while you ride?
Also, if you are not strong in your core, it can cause you to collapse forward at transitions.
Ride along the centre line of the arena (get away from the boundary fence), and take a kind of snake-like path. But don't turn the horse so that it is along the line, try to get it to always face straight to the other side of the arena... Press your right leg against the right flank, and at the same time put more weight in your left stirrup; the horse should move laterally to the left while still moving ahead. Then do the opposite: left leg against the left flank, and at the same time put more weight in your right stirrup.
Making your horse move to the side like this is not just useful for moving it away from the fence so that you don't whack your foot against the poles, but also to move to avoid manhole covers or low branches.
Thanks all. Past few lessons have been better, horse is still being really lazy (I still think he's great and think he'd make a wonderful privately owned horse as I think he's just bored) but my position is improving and the instructor is happy with how I'm doing. He's stopped trying to amputate my legs as much too which is progress. I'm somewhat restricted in what exercises I can do as it's at a riding school so I have to follow what the instructor asks me to do but we're getting there.