In a word NO.
You have to send your driving license, both parts, to the Embassy with a covering letter and fee.
See the attached link which tells you exactly what to do.
Once License is verified, then you have to exchange it for Korean License, nearest DVLA centre is just before Masan.
Note that you will have to hand your UK license over, unless you can prove you are travelling and need it. Otherwise you will have to make the trip back to Masan when you have travel arrangement.
Driving on Geoje is an art....just keep a good eye on your rear view mirror..... Good Luck