I used to think this browning was down to the wind coming from a certain direction but on a gardening programme once it said that this is caused by an insect and once the browning has occurred cannot be cured.

Welcome to Goy. There has been a lot of discussion about this on here Newby. If you post a photograph then I'm sure someone will be able to give you some advice. Are other leylandii hedges in your area also affected. Has there been any changes in the micro climate recently eg.a tree felled nearby allowing the wind to get at it. Are the patches from the bottom up or dispersed about the hedge.