We have this too.  The previous owner saw it somewhere, thought it looked pretty and so dug some up to replant in her garden - big mistake!!!
I spray it at least once a year and it really does do a good job.  Digging up is okay I suppose, but only really doable (sp?) if you only have a little.  When I do dig some up I carefully place the roots out to be burned or killed by the frost.    Even removing them to the fireplace is dangerous, as if even a little avoids being burnt, of falls off the wheelbarrow, you'll have a new outbreak in a new place.
Our sheep eat it, as do our rabbits, and I keep thinking I'll try it too.  However, I prefer to let it grow so that I have more leaf available to let the poison get down to the roots.  I reckon that in one area about 95% was killed in one spraying.  The rest WILL regrow and replace, so do not stop.
The frost kills it too.  The first year here I wondered if a kindly neighbour (or embarrassed previous owner, had crept into the garden in the night and sprayed it).
Since experiencing it myself I have become hyper-aware of it (obsessive maybe?)  and see it more and more on motorways or small bits of waste land.  
Beware.