It depends on what kind of weed killer it is, Kev. Can you tell us what the active ingredients are? In the U.S., they're listed on the front label--I don't know about in the UK.

usually it means on the leaves. if the weed killer is inactive once it touches the soil then you can use it to kill of weeds under the hedge. if it remains active then don't use it.

Or at least tell us the name of the weedkiller...

Some weedkillers such as glyphosate and a commercial version Roundup act by being absorbed by the leaves so spraying under a shrub is OK as long as you don't get any on the leaves of the shrub you want to keep. . If you do get a splash on them you can rinse it off straight away with clean water.Total weedkillers on the other hand kill anything they come in contact with and kill the roots, so they would kill the privet.

The first kind usually say systemic somewhere on the label, and the other kind usually say total weedkiller.
Hope this helps.

Oops, sorry, that doesn't answer your question does it?
I'd either get a different weedkiller or ring their customer service line.

Just what kind of weedkiller can you use around the garden but NOT on privet? When I wanted to kill privet I had to cut it down then use SBK stumpkiller on the stumps!

I have seen trouble with products containing glyphosphate (RoundUp) or trimec (most selective broadleaf weed killers). Both are supposed to be inactivated on contact with soil, but can be absorbed by the roots if they are sprayed to the point of runoff, especially on sandy or highly organic soils. In the case of the latter products, Privet is one of the more sensitive species, and will show curling of the leaves with only mild exposure, though it rarely kills the bush.