Cropping of grass and vegetation before the growing season(hopefully not within it...) is useful to allow identification of and access to the knotweed(for spraying, treatment and destroying or removing).
This of course allows the underground rhizomes to spread and will do little to affect the deeply-buried and fragile rhizomes already extant. Root crowns are easily identifiable; however, the tiny white cilia-type "micro roots" arguably require a practiced eye.
The growth in these images will have to be engaged with in the knowledge that further growth and spread is initially likely if the soil is disturbed...but given that it is this knotweed that is in most urgent need of remedial action, isolation of site by a barrier(fence)would be an immediate and positive step.
This would effectively reduce further unwarranted disturbance of the knotweed...and would both inform public of its presence and of the owner's willingess to engage in a fully informed way with the problem.