Following the announcement that EasyJet is to launch flights to Split and Dubrovnik from London Stansted Airport, I did some research about the new flights and their suitability for further travel to Korcula:
If you would like to reach Korcula on the same day and avoid staying overnight in Dubrovnik, you would need to take the Easyjet flight from London Stansted to Dubrovnik.
The flight departure from Stansted is at 07.30, arriving in Dubrovnik at 11.30. That gives you enough time to reach Dubrovnik Bus Station by 15.00 to take a scenic bus journey from Dubrovnik to Korcula.
On your way back, leave Korcula by bus in the morning at 6.45 am. You will be in Dubrovnik at 9.15 and still have enough time to reach Dubrovnik Airport, as the flight from Dubrovnik to Stansted leaves at 11.50 am.
Have a look at below timetable sample:
If you would like to fly from London to Split Airport and would like to reach Korcula on the same day, the best option is to fly to Split from London Gatwick. The flight departs at 06.10 and arrives in Split at 09.40. To fly back from Split to London, book a Split to London Stansted flight (departure 21.20, arrival Stanstead 23.00). In this case, you will have enough time to do some sightseeing in Split and catch the fast ferry catamaran from Split via Hvar to Korcula (departure 17.00, arrival 19.20). On your way back, use the same ferry service to reach Split from Korcula. (Check detailed options from Hvar)
Have a look at the timetable below: