They like warm conditions and are best grown in a greenhouse in the Uk. You can grow then outside if in a warm sunny spot and protected from the wind but you may find they do not produce much fruit.
It is probably going limp because it has not been outside before and is not used to the direct sunlight and different conditions. If you do not have a greenhouse then you will have to leave it ouside and just see what you get. If you google growing aubergines there are plenty of sites with some good tips.