Trickyh78 - it can be enlightening to escavate the soil; hard work, but enlightening. I have found sections of wall where there has been no wall that I knew of. In the garden of a 'new build' house I even found a pneumatic drill bit. I've got sections of terraced garden in the place where I live now, and the back-fill of the terracing has sections of rubble with voids. The terracing has been in place for maybe 3 decades. You always find surprises in gardening
I'd cut those privet back hard (look for dormant buds near the base of the woody structure) and give them a good feed of something. Pelleted chicken manure, anything. They may come through, they may not. In my books on hedges - make sure the ground is thoroughly prepared. That could mean quite a bit of digging and other preparation for what is 'only a hedge' in some peoples' minds (although I do not assume you are one of them!). Most hedges don't necessarily flower, but a hedge is a long-term feature/structure and you don't want to be trying to replant it every year. It isn't summer bedding. In many ways, a hedge can be a longer surviving feature than a brick wall (let alone a fence).
Ragarding pruning - do you still have a local library? If so, there may be some good books on the shelf which give pictorial demonstrations/examples (a picture being worth however many words). RHS publications are worth a read. I think they do (or have done) a thin tome on training and pruning, with a lot of info condensed into a relatively small book.
Good luck with the hedge.