I strongly suggest you look into the ESL programs offered by the various boards of education. Their instructors have at least a a Bachelor of Education and a post grad diploma. Private schools have laxer standards. (My wife has taught in both)
All the boards offer adult programs and the cost is usually better than the private schools too.
I agree with sum_guy above. Private language schools are quite expensive. There are education agencies who basically help them advertise overseas in countries with high demand for learning English.
I have some friends who came here on working holiday visa or study permits. Frankly how well you improve in English is mostly a matter of how much practice you get. Some people can probably spend 10 years in English school and still not be fluent. To me, the real value of studying abroad is to make friends and learn the "natural" way. So with this in mind, picking the right school probably matters less than social habits and shaking off the shyness.