Ooh, no easy task that. If the ivy's been present for a while, it will by now have roots everywhere - the only way to get rid of it permanently is to cut it all down to about 1 inch, then dig around and cut into or drill into its roots and poison them with something like SBK brushwood killer. But, and its a big but, its a risk doing that because of the hedge and its roots. Unless you want to replace the hedge, when you can deal with the ivy at the same time, I'm afraid you're reduced to cutting it down and extracting what you can by hand, year on year. Spraying the ivy foliage with glyphosate won't be very effective - it may kill a few top stems and leaves, but won't kill it back to the root, and spraying also endangers your hedge.

Oh crumbs ! It's actually next doors hedge think I'll leave it for them to sort! They are looking into it, thanks for the reply though!

I loved the ivy in my hedge and so did all the nesting birds and the hedge was nice and thick. My neighbour pulled all his out and has suffered with gaps ever since.