Stem injection looks promising.
But I don't really want this carcinogenic poison glycophosphate sprayed liberally around SE23.
It is linked with other problems too: "ranging from birth defects and kidney failure to celiac disease, colitis and autism. "
And it affects honey bees and butterflies.

http://www.theguardian.com/cities/2015/a...ies-use-it

Knotweed must pop up in people's gardens all the time, and not knowing what it is, it will be successfully defeated along with any other weed, by the usual methods. It is persistent, but not close to indestructible if it is caught early.