Hmmm.. I'malso having bramble root trouble!! I pulled mine up several times over the last couple of years but they keep coming back coz their roots are coming from under next doors fence I would try some weed killer like people above have suggested but I have pet rabbits and don't want top poison them!
The other weeds I have trouble with are that horrid long grass with creeping roots (couch grass?) and something that sends runners and has strawberryish leavesbutnifruits or flowers. These two just spread around my gardenfaster than I can pull them out!