Hi welshfox, As you've obviously found out already, it's an extreamly dificult weed to eradicate! It is resistant to most weedkillers but herbicides that contain the chemical 'Glyphosate' seems to be the most effective, although the underground creeping stems (Rhizomes) can take about 3 years to die after repeated applications.
I think the best approach is to keep cutting it down to ground level then spraying the fresh re-growth and try to exhaust the plant that way, then when you think you've got it beat dig out (ALL) the rhizomes and root fragments and burn them on site.
If it go's into a landfill site, your local authority needs to be notified, as it needs to be buried at least 5 m deep.
You should be able to get some good advice re control, disposal etc from the Environment agency, as I believe it is a notifiable weed subject to strict procedures. Good Luck Tbird+