Hi Kathryn and welcome to GoY. I feel for you, after losing a lovely thick hedge very similar to yours to my over enthusiastic neighbours attentions. I found the only way I could regain the privacy that it once gave us was to cut down the existing trees and re-plant with 12 new ones.
Good luck and I'm sure other members will have plenty of good advice for alternatives.

if you want a conifer hedge - replace yours with Yew, it is fairly quick growing, can be pruned to whatever height/width you want and if it gets out of control - or the builders come back, it can be pruned hard to rejuvenate. Most conifers will die if cut hard, they don't re-grow foliage, so you will need to get them out. Planting among them will be difficult as they will have taken up all the root space and moisture. If you have to leave them, maybe try a vigorous ivy like 'Gloire de Marengo' it has big glossy colourful leaves.

Yew is not a good choice if you or your neighbours have children or pets as the leaves, seeds, twigs, bark and roots are poisonous.
If your property borders grazing land and cattle eat your yew hedge you are liable for their demise.

Advice is there to be taken but not necessarily acted upon.