Products in the Middle East are usually 220 Volts, with the two pins like Japan. I know this from many years of blowing out electrical appliances with wrong voltages (I live in Saudi Arabia). However, I don't know if there is any different adapter released for the Middle East...just saying that you might want to check the voltage on it first. If it is 110 Volts, there are two things that can be done:-
1.> Buy a step-up transformer as the above post says. Just plug the adapter into the transformer, and the transformer into the wall. A transformer should cost fairly cheap and should be easily availabe at any electrical store. This has the advantage that it could be used for any 110V product.
2.> Just buy the official Nintendo DS Lite adapter for UK. Probably a little more expensive, since it is official, but then you can use it just the way it is meant to be.
Hope that helps.