I would not cut them back now as you do not know if there is wildlife in there nesting.
Leave it until August for the safety of the birds and other wildlife that are in there.
I do mine in the last two weeks of August every year.
One thing I forgot, what type of hedging is it that you have?
Another thing is, Deciduous or evergreen?
If deciduous then have you thought about getting it laid to make it stronger and more beneficial for the wildlife?