I've been to Thailand a couple of times. My shortest trip was for a week. We flew in from South Korea for the Chinese New Year holiday (so not really jet lagged at all). We flew into Bangkok, spent the night in Ko San Road (which is a crazy eye-opener for the first timer), and then flew down to Koh Samui the next morning. We enjoyed Koh Samui and made it over to Koh Phagnan for a night or two as well. After we were rested flew back to Bangkok and on to South Korea. With double the time you could do double the places, but remember you'll probably be jet lagged coming all the way from London. How long is the flight?