We have had a similar problem with our 11 acre wood - it took the best part of 2 years to get to all parts of the wood! We have in the end invested in a tractor and a Bomford rotary slasher - a sort of industrial strength Flymo for the back of the tractor. We were cutting paths by hand and they were growing almost as fast as we cut them. This way we can clear areas, and by cutting regularly the brambles do finally get the message and get crowded out with wildflowers and grass. It takes time though.
In terms of wildflowers, we have used glyphosphate on the advice of both the Warwickshire Wildife Trust (we are a LWS/SINC) and also the Forestry Commission to kill back grass and other weeds. We scarified the area as advised...and grew a wonderful crop of dock! Now we are killing it off again, scarifying again, and will continue the cycle until the dock gets the message and we can grow wildflowers instead. We were advised that the alternative is ploughing but we don't want to do that because it will damage the tree roots and topsoil. We didn't want to use weedkiller of any kind, but that was the advice we had.
We don't know how effective it is on brambles as we used it in a clearing area not affected by bramble.