To get rid of Japanese Knotweed you will have to get it professionally done the link below is the environment agency's advise
http://www.environment-agency.gov.uk/static/documents/Leisure/japnkot_1_a_1463028.pdf

Hi Hywel.....I am currently tackling this too. I have been provided a very lethal weedkiller and instructions from a friend I know "in the game" I am trying to tackle myself as I only have 2 crowns....at the very back of my garden so out of the way of the house. Theres lots of information on line, like the link above. Most sites Ive seen for treating yourself say to use glyphosate based products. Theres also info on the SEPA website (but think they are just for Scotland??) . It can be VERY costly calling in the proffesionals. Karenfrance also has the dreaded stuff but again shes in another country with different laws. The main thing is to be VERY careful with any bits you cut off - straight into a bin bag (mines are in an old compost bag) - then burn. It is treated as hazardous waste and cant be composted or dumped as the slightest slither of the stuff sprouts and grows...x Best of luck to your friend.

Yes I agree. You do not remove any parts of Japanese Knotweed from the place where it is growing. You keep cutting down the new growth and burn it or dig it out and burn. Treat with Glysophate (paint it on new growth). It takes 3 years am told till you are clear. A Scottish gardening programme called Beechgrove Garden had an article on it a few months back in Edinburgh:

http://www.thebeechgrovegarden.com/images/factsheets/2012_Template_FS5_1.pdf

Hope it helps!

Our son tackled it by cutting off the tops and pouring weedkiller into the hollow stem. No use using glyphosate for that though, you'd need a deep root weed killer. If the problem is coming from outside the garden it won't be permanently solved until its all be cleared though.If its on public ground the council may remove it.

Thank you all. I will give the information to my friend.