Thanks, cutteduppear - I appreciate your thoughts.
I agree that it seems to be propagating itself via running roots, which does suggest that Leycesteria might not be the answer.
What is odd is that it reminds me of something we used to have in a border, but we "eliminated" years ago because it was throwing up runners everywhere.
I may have a plan of the garden dating back to then that we inherited from the previous owners, and that was done by a professional garden designer, so it should be definitive. It is just strange that it might have reappeared after a gap of maybe 10 years.
I do feel fairly happy that it isn't Japanese Knotweed though. I know that some was found a few miles away from here, but not near enough to have found its way to us, or so I would hope.
Anyway, I mowed on Saturday, so the Triffids have gone for now!