I'd suggest it's probably powdery mildew, which is a environmental problem, caused by our changing, less than ideal weather. It causes brown patches and damages the leaf but it's something that should improve on its own. So assuming I'm right, you only need to give the hedge time to recover although you can cut off the ugly bits if you like.
Like mort says maybe it'll improve on its own, it's more of a preventative measure to make sure it doesn't come back. My friends Laurel hedge had a similar affliction bordo mix helped it back to health and it thrived thereafter.
I have read somewhere that a 60/40 water/milk mixture helps.. It spreaded to my newly planted magnolia and it worked there, I tried it on the hedge but I think it is to badly.. Added some hedge fert mix on ground.. Hope it recovers soon..
I've cut the hedge back alot this year so I guess the ground was a bit depleted to give the hedge what it need to recover..