We have bought a new house with a Leylandii hedge that has been unpruned for several years, trimming the height is no problem but the sides have about 3 inches of green and then brown inside. I'm under the impression that if you cut back in to the brown stuff the green won't grow back....Ideally I'd like to cut the sides back by about a foot but not if this leaves me with a brown hedge. Any solutions?

It should be fine, if you do cut it back you can always just add extra plant feed for a week or two just to give it that extra boost to regrow. We cut into the brown branches on most trees and it doesn't cause them any long term health issues.

If you are worried then in the weeks following, just make sure you give them extra watering and a little bit of plant feed, this should compensate for the loss of greenage.