Check out Satya Movement Arts for a list of yoga, pilates and dance classes in Seoul taught in English. Not all are open to the public and you might want to contact individual instructors to makes sure the schedule is current.
Also check out Pure Yoga, Jai Yoga Center and Magic Pond Yoga.
I took classes at Pure Yoga and I am doing the Yoga Teacher Training Program at Magic Pond. Jai Yoga Center brings in internationally-known instructors and has some prenatal yoga classes as well. I haven't taken there, but I have me the owner and would like to take from her, but all of my time is focused on Magic Pond right now.