I have no idea how prices compare to what is already available in Phuket, but I recently came across this site
http://www.tv-air.com/promotion/airfare.php?id=202 (recommended by
www.mangosauce.com) whilst looking for cheap fares for my GF to get to England. I know it states prices from Bangkok, but I would imagine being a travel agency they could quote prices out of Phuket airport. I notice that they currently have Singapore on offer for 4,300baht but as I say, that's out of Bangkok.
Worth a try ??