Here is the link to the Korean Embassy in the UK:
http://www.koreanembassy.org.uk/engsub2_1.html
These are the required documents for the C4 visa as found on the website for the korean embassy in the UK, but please double check to be sure there are no recent changes to the policy. The policy in the US has changed very recently and not all the consulates there have correctly posted the changes. Like US citizens, I am guessing that Korea requires background checks from UK citizens, too, but I don't know this to be fact. Here is the current list:
- Employment contract
- Letter of employment recommendation issued by the head of the relevant central government agency, an official letter from the relevant government agency or documents proving the necessity of employment.
* Visa Fee : £15
The fee is waived for British passport holders. / U.S.A. Passport Holder : £ 22.5
* You may alternatively submit the following documents.
- Certificate for confirmation of visa issuance issued by the Ministry of Justice in Korea