Our neighbour has been struggling to control his bramble patches for years. He keeps cutting them down to the ground and they just come back. On the other hand we no longer have bramble patches, but it's taken a lot of effort. Basically strim round each patch and (with a sharpened small spade) cut through the roots about 4" down and pull them out. Strim around again and remove more until the patch has gone. Then repeatedly mow the area and dig out any strong growth. We started by removing about 10,000 many of which had roots both ends. We now remove perhaps a dozen every year.
The annoying thing about brambles is some are below cutter height and you can trip over them. Walking around our place used to be a real hazard.