salts good but its not selective

It might be a Campsis variety, but the problem you've got is the roots are under the paving. You can kill a plant at the roots by exposing them, drilling or cutting into them and applying neat SBK (carefully, without getting it everywhere), but if you can't access the roots to do this, it won't be terribly effective to just broadcast it on the paving.

Sounds like a Convolvulus. It may have been planted by the original owner or it may be a weed that was growing there.

all plants need the sun

I thought convolvulus (bindweed) too, as its very deep rooted and hard to destroy. If its well away from plants you care about you could try a total weedkiller like Pathclear, but not if there might be runoff onto plants you want. If it is convolvulus it will probably need several applications, being extremely deep rooted and determined. For the plants that are growing in the beds try training the shoots up canes. When there is polenty of growth lay a plastic sheet or spomething over the surrounding plants and spray carefully with Glyphosate. This also will need repeated treatments so don't lose heart.

Put Bindweed Images into Google - most of the pics are of white ones but there are a few pink ones.