Lleylandii trees

sodium chloride will kill any type of plant

Thanks Chip, but isnt that just salt? and could it really be powerful enough if sprayed on big leylandii, to kill them off?
littlei

Depends on how much you put on and how soon it rained after you put it on. I doubt your spray would go all over a Leylandii unless they are small new plants.

Littlei,
The culprit may be the cypress aphid, a 4mm bug which sucks the sap of leylandii and other conifers, turning twigs and branches brown. This was recently reported on the national news and wide spread across the UK.
The Royal Horticultural Society, which has completed a two-year study into the pest, believes the UK could be suffering its worst outbreak for more than a quarter of a century. It blames the mild winters of the last decade. I would tell your neighbour to send a sample to the RHS for analysis.You may be due for an apology.

Thanks for that answer Ams...
This sounds like the most likely cause, and if I were speaking to my neighbour I would tell her to do just that.
In fact I may drop a note in her door.