I have a number of leylandii that had this problem last year. I hired a certified arborist who told me they had two problems: 1) bagworms and 2) they were suffering from some winter damage due to an unusually cold and frosty winter. In addition, he suspected some spider mite damage from the previous season.

Leylandii often do not turn brown for some time after the damage has been done, so could it possibly be from a problem that occurred last summer or fall?

You need to check for the conifer aphid, are there any signs of sooty mould, go in a few inches to check for this, and the parts of the conifer that are green need to be checked to, do it now, catch it before its to late, normally once die back occurs it wont return, in the past ten years have noticed a big increase in the conifer aphid, Spray with bug clear its very good, i spray them at least four times a year in the gardens i manage.