It may be ages since this was posted - but just to say, that in my last garden, I had a real problem with an area of couch grass! I covered it all with cardboard boxes spread out, and, though it took at least 2 seasons, it worked well. I then planted potatoes in the area, they grew just fine, and were yummy when harvested. The best bit was that the ground after they were finished, was lovely! I DID add lots of manure when I planted them, but certainly didn't have any more grass after that.
I have also had success with getting rid of creeping weeds by putting covering over autumn and winter with cut up compost bags. Keeping the light out long enough is the secret.