Dan, If bramble berries are similar to black berries (and I believe they are), they have very shallow spreading
roots and do not like competition in the
root zone. Blueberries are the same way. Because of that, I am planting only tap rooted guild plants with my berries, including comfrey, mustard, and horseradish. None of those would be considered ground covers, of
course. I have only pine
straw and oak leaf mulch around my berries, and to that I add leaves from my guild plants (chop and drop) so the berries get to have all that shallow decomposing goodness for themselves the way they like it. The only tap rooted ground cover I can think of is purslane, but it's
water needs are very different (it likes it dry). You're in a very different climate than I am here in Florida, so maybe there's some other tap rooted ground cover that I'm not aware of.