Unfortunately, British citizens do not qualify for the pension refund. However, under the contributions agreements, you can request that your pension payments be added to your British accruing pension credits in the UK, of which you can begin to receive when you retire in that country.
The procedure should generally be the same, but talk to the local pension office for more detail (this is the main office, but there are several offices in Daegu (if you happen to teach here), they should be able to give the locations of others):
Address: Kukminyeongeum Daeguhoegwan Bldg.(국민연금 대구회관) 1198-5, Igok-dong, Dalseo-gu, Daegu
Zip Code: 704-713
Phone No. : 053) 589-4516~7