Ahhhh...iced tea. I live on it in the Summer. You'll never break a Tennessee girl of that.
The irony is, good quality, strong tea like you often get in the UK is likeliest to go cloudy (the cloudiness is tannins). That supposedly doesn't affect the flavor, but you won't convince me. Cloudy tea is...meh. Cooling it down too fast will cloud it, too.
I buy the cheapest, nastiest own brand tea in the supermarket for iced. The kind that's, like, 80p a box. Two bags in a big tea pot, with sweetener and a few cloves, if desired. Usually, I end up mixing it with what's leftover cold in the pot from my husband's expensive loose Assam. The two together are just about the perfect flavor.
Since refrigerator real estate is so scarce, I often leave my big tea jar out on the counter with a lid on and count on the ice for chilling it. It keeps fine.