Thanks all.
I'm near Chepstow, and there doesn't seem to be any LA help that I can find.
The patch is next to a stream, so spraying isn't an option. Being next to a stream also means treatment isn't guaranteed, as more knotweed can and will wash down when the stream floods.
Perhaps I'll keep cutting and burning, and try a bit of stem injection towards the end of the season when the fluids are being drawn back down to the roots.