It is not against the law to do anyting with it. It is prohibited to encourage its spread or remove it from a site. You can kill it off using a weed killer without breaking the wildlife and coutryside act.
Glyphosate works but needs to cover all of the leaves up to about a metre high to be effective.
I've had it for years and in fact left a row of it at the bottom of the garden to hide the neighbours but this year I'm trying to get rid of it by weakening it. I'm digging up as much as possible with each spear that comes up.
To be fair to the Knotweed it is attractive but it will advance up the garden and every bit left in the ground sends up new spears.
My new neighbour had all of hers dug out and a new lawn laid - months later up it popped again through the grass!
we have some in the field near us and the estate treat it every single year by professionals and each year it comes back..Even petrol and setting light to it will not get rid if it I;m afraid! Its just impossible!!! You just need to accept that and try to control it!
It is illegal to dispose of it incorrectly though..as the smallest piece of root can then become a plant so be careful!
Japanese Knotweed is particularly difficult to get rid of but if you are prepared to keep working at it you should be able to get rid of it yourself. I had a similiar problem and a friend recommended using weed killer after cutting down the weed as much as possible - very hard work but worth it in the end! This site was useful when I was looking for advice and the product seemed to the trick. It also tells you how best to use it to solve the problem. Don't envy you the task having done it myself but good luck and hope the site helps!