Hi ballistic,
I work with trees for a living.
Itwould be most helpfull to know what the plant be-deviling your brickwork actually is, or some pictures of it would help alot.
No offense to sonnyboy, but don't use salt! It will leach into the surrounding soil and nothing will ever grow where the salt concentrations are high for several years.
You want a systemic plant killer like glyphosphate, the generic term for Monsanto Corporation's product "Round-Up".
Unfortunately, it works best sprayed onto the foliage, the plant absorbs it and sends it down throughout the root system and kills it by destroying the plants growth regulator hormone, causing intracellular collapse.
However, you have removed the foliage, but all is not lost. If the plant is trying to sent out new shoots from the areas you have cut or torn back to, (very common with vines and other hardy shrubs), you're still in business.
Try to identify the cambium layer of the woody tissue you have cut back to. That is the outermost growth ring just inside the bark layer. Apply glyphosphate UN-diluted directly to the cambium layer. Use heavy rubber gloves, and don't spill the product on the soil or any desirable plants. If you have cut back to several places, hit them all. Dab it on anything new and green the plant is sending out.
The product will work mor slowly than if you still had foliage to work with, but you should see it spurt up wildly, then collapse.
Hope this helps.
Eric