Theres a lot of old wives tales about JK .(It grows through concrete floors
In my experience systemic weedkiller will do for it?
Eg roundup or even better the same stuff from Wilko for 1/3 the price.
Wait til its actively growing dont knock it down ,give it a good spraying. youll find that the main growth will die back in a few weeks. If you see(and you probably will) new young growth zap it again (dont chop it up).If you keep zapping it with the WK it eventually sends up the white flag.