What you have is Helxine and it does tend to colonise where happy. If you
have a flame gun or one of these weed wands you can destroy it without the
use of weedkiller, clean and effective.
It is actually a useful little plant in the right place.
HTH Jim



Many thanks for all the answers. Unfortunately for it (the plant) I do
not want it where it is, so it will have to go. Maybe we'll dig a bit
up and grow it somewhere else, but it definitely must go from from my
tidy, weed-free driveway.
In limine sapientiae