I found the following page useful for identification and treatment:

http://www.ayrshireriverstrust.org/cisp/...-knotweed/

I understand that cutting it back is bad as it needs to grow to transport glycophosphate weedkillers to the root system, but looking at Siddons, I don't think they can be doing much to control it as the plants are really big and covering a large area.

The injection method sounds good though. Maybe I'll suggest they try that.