Thank you InOban - Agree inject it - stems are hollow.
New method should be the answer - no poisonous chemicals!
I got rid of it in my garden - and the neighbour's that it was spreading from.
You can use glyphosate etc., but they are best with adjuvents (something like PVA glue) which stick the herbicide to the foliage and gives it longer to be absorbed, or instead inject it into the hollow stems as said above, but it is still glyphosate (and probably a pain to do!)
My system was to cut it off a bit above ground, then put ammonium sulph
amate powder into the hollow cut stem. The explanation was that ammonium sulphamate is sulphate of ammonia (fertiliser) "made crooked" so the plant takes it right down into the roots and then gets killed by it. I bought it under the name of "Amcide." Not cheap though. Of course, it's no longer available as a herbicide as no-one will fund the testing required, but if you buy it as a compost accelerator it is still available!
This worked in one year, except that a few spindly bits came up the next. Cutting them off and putting it on the wet surface again seemed to complete the job. I suspect this method wouldn't work on a wider scale though, as the manpower costs would be too high for it to be viable.
A