From Sam: "I am interested in a career change as I have been working in a UK university for the past 5 years and have recently completed my PhD and I would like to work in Korea. I suppose my biggest concern is landing the first job and ensuring that is a decent experience. In your experience, is there a good company/agency that you would recommend I contact to ask about positions? I have seen jobs on Dave's ESL but there are so many and it would be good to have recommendations. It would be good to go through an agency that offers visa and housing etc."
If you want to work at a Korean university, it can be very difficult to get these jobs from overseas. That said, I have no idea what your PhD is in, so perhaps you want to teach sometimes besides ESL. If this is the case, you might have better luck finding a job from overseas, but as far as agencies or companies to recommend using, as far as I know there are no recruiting companies that place people in Korean unis. Everyone just finds their jobs through searching online for school's advertisements or by networking.
A word of warning though: Korea is still kind of the wild west in a lot of ways when it comes to teaching jobs. Plenty of people get ripped off, especially those that don't do their research, and it's quite obvious that you have not if you don't know that people don't get uni jobs through an agency, or that almost all teaching jobs in Korea include housing or that all jobs include a visa. Even though you have a PhD, because you a foreigner and a newbie to Korea, you will be at the very bottom of the totem pole here, even lower than the department secretary or the security guard on campus. And, you will find that academic standards are shockingly low here so for someone who is a "real" academic, you might find it to be a tough place to work.
Check out my book: How to Get a University Job in South Korea: The English Teaching Job of Your Dreams,which although it is geared towards English teachers, you might still find helpful. That's not to say that you shouldn't teach here, but just be aware of what you're getting yourself into.