Knot Weed
Knot weed is probably the most persistent and most difficult to kill off of
all the weeds we have in the UK – it spreads vegetatively and according to
rumour has been known to cross under motorways. You should keep treating
with a heavy duty systemic weed-killer such as SBK (UK brand) by painting
all the visible leaves as they emerge – which they will start doing in a
month or so, I guess, depending on where you live. You won't get quick
results but you will eventually kill the infestation off. Don't forget to
check if your neighbours have the infestation as well and get their
co-operation. Do not, no matter how organically inclined you are, think you
can get rid of knot weed by digging it out – the roots go down a very long
way and re-generation is possible from incredibly small fragments. There is
one other way of eliminating the problem – move!
Sorry not to have better news – good luck