Laying hedges is one of those magic things - you hack your hedge to within an inch of its life, then next spring it bounces back all fresh and green, thicker than ever. It's hard on the elbows though.
It depends how you want your hedges to be. If you want big thickets for all kinds of wildlife to live in, and you have the land to spare then a few bramble patches will be ok. But brambles take over so I certainly wouldn't let them stay the whole way through the hedge. Even our cultivated brambles keep popping up inside the polytunnel, and in the middle of rhubarb plants. Because I hate the stuff, I wouldn't leave blackthorn in there either.
Are you sure they are brambles and not wild rose? If there's rose, then leave that as it's pretty and provides hips for winter feed for the birds.