Children are like sponges. Korean kids (elementary school) learn English quickly and with no accent when they go to school in Canada. Teenagers have a more difficult time. I think an all English environment (at least for part of the school day) with native English speakers is the best method.
I know of situations where English tutors have been invited to live in Korean homes. Some Korean mothers actually move to English speaking countries for a period of time. English academies provide reading, writing, listening and grammar skills but don't always produce good speakers unless there are an adequate number of native speakers on staff.