Firstly you need to be aware that the shortest route between the UK and South Korea doesn't go near to any hot countries. It's illustrated on the map here:
http://www.gcmap.com/mapui?P=LHR-ICN
Looking at that map, and trying to work out a reasonable detour from that route, my first instinct was to back Mushroom25's suggestion of Dubai. However, checking the schedules on the Emirates website shows that the return flight to Heathrow takes 7 hours 30 minutes, which is beyond your maximum flight time. (The outbound flight is scheduled to take 6 hours 50 minutes).
Dzug2's suggestion of Turkey makes rather more sense, as would Egypt.
Chris