In reply to Dan Arkle:
It's one tough weed but there are companies who specialise in dealing with it. I've seen it grow maybe 10ft in a couple of months. As far as I can remember it takes possibly upto a couple of years, during which you can't plant anything, of cutting back and spraying new shoots with killer!
I learnt this from Help my House is Falling Down BTW - channel 4/4OD.
The problem could be that it's not upto you but your potential neighbour who may or may not be bothered - especially if it's rented etc. I also think mortgage companies don't lend on houses with knotweed.
There we go. Those Victorians have alot to answer for...