We get lots of questions about removing Buddliea plants growing out of you house and garden walls. They are one of these special plants that can grow just about anywhere their is space, in walls mainly created with lime mortar or in railway sidings. They seem to require little or no soil so get a foot hold and then they are away growing at a fantastic rate.
To remove them from a garden wall the best way it to cut them back flush to the wall and then us stump killer applied by drilling holes into the stump and poring the chemical into the remaining stem/stump
Its not a good idea to try to dig out the roots in a wall as you will find that they are extensive and you will only damage the wall. Once the Buddliea is removed from your wall the next operation is to re-point the wall to stop any further plants becoming established