If you are a native speaker, getting a teaching job will be a breeze. If not, then it will be quite tough. Also, it would be advisable to get jobs directly through the schools and not recruiters and agents. Scammers abound here. Visas may be a problem though. Heard that it's not so easy to get it in HK anymore. It would be good to check with the school if they can do this for you. And prepare yourself for the culture shock because Korea and China are two very different worlds. 

Thanks for the quick response! Yes I'm native, from England. Ok that sounds reassuring, just a case of persevering and applying. I have been there twice on small visits and was like a deer in headlights...you stand still you get swatted. Looking forward to the undertaking though.

Thanks once more.

With your degree, previous experience & TEFL you fulfill the requirements for an FEC/work permit. The only current issue you'll face is having to apply for the Z visa in the UK. Try not to use agents to find work as they sometimes take a cut of salary. Make sure your contract is directly with the employer. Good luck! 

prepare your list of questions for any potential employer and don't be afraid to get things clarified: i always double check their answers 

don't be deflected by their answers.

ask for photo's of accommodation.

the only stupid question is the one you don't ask.

Best of luck in your search