I have seen some english instructors giving beginner lessons. The way they explain the turn to their students is to use the inside leg as something for the horse to "bend around." No actual pressure is used on the inside unless the horse doesn't properly bend into the turn.
They also instruct student to look and "point their navel" to where they are going. This has the effect of shifting weight in the seat and applying pressure with the outside leg.
From the body/leg position, this all seems very similar to western riding. The big difference in the english vs western turn is in the hands/reins which is accounted for in the bit design.