I'm assuming the original poster means bindweed, not aquilegia. When I moved to this garden, admittedly 18 years ago, it was infested with bindweed, to the extent that one wall, about 20' long by 12 ' high, was covered with bindweed and ivy. Over the years, I must have dug out miles of the stuff, and now only get the odd tiny little wisps coming up, which I pull out on sight. However my soil is very light and free draining, it would have been much more arduous on a heavier substrate. I'm not a fan of weed suppressing membrane either, but you might want to consider a technique recommended by Alys Fowler, of putting down a thick layer of cardboard ( she suggests bike shops as a good source) and covering that with at least 15 cm of organic mulch. The cardboard will suppress weeds, but will also rot down. If aquilegia's the problem, just dig it out.