Answer: Privet bushes (Ligustrum) are vigorous growers needing numerous shearings during the summer months when they have their greatest growth. They are tolerant of extreme pruning, so I would just cut them down close to the ground right now and be patient while they re-establish themselves. It may take a few years to get to their present size but that will give you a few seasons to work on their shape.
Always make the top a bit narrower than the bottom (a VERY moderate teepee shape) of your hedges. By doing this you allow the sun to get to the lower branches making them fuller, greener and better looking. It is possible that was part of your problem. If the lower branches had been stronger, they may have held up better.
The next question you should ask yourself is whether the privet is in too exposed an area. Although privets can usually tolerate pretty extreme weather, even they have their limits. Keep them thick and not too tall.
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