Neighbor has Japanese Knotweed

Just sorting his garden could be a very lengthy and expensive operation. Just disposing of the waste is a job for a professional set up. However there does not appear to be any very conclusive answers for the OP. This article https://scsi.ie/wp-content/uploads/2020/11/SCSI-Knotweed-Guidance-Notes-2.pdf gives some information.

IN THE UK If your neighbour has Japanese knotweed on their property, they are under no legal obligation to remove Japanese knotweed from their own property. However, if it starts to encroach upon your property they are causing a private nuisance and therefore are open to court action.

https://www.japaneseknotweedexpert.co.uk/faq/neighbour-has-japanese-knotweed/

It is difficult to find information for Ireland but presumably the situation is similar to the UK. Taking your neighbour to court doesn't seem like a very useful (or kind) way of approaching the situation.

How many gardens are affected - yours and the house between, what about in the other direction and off the bottom of the garden? Could you all get together and offer to treat the whole lot? A group might have more chance of nagging the council into action also.

Don't stop treating the stuff in your garden or it will very quickly get out of hand.

Round-Up is the best option. Start spray now, then again mid Aug and then again at end of Sept.

That probably will be enough, but you may need to repeat next summer/autumn.

Ask the neighbour if he will allow you spray his side too.

Best value is a 5L drum of roundup from the agri shops like Liffey Mills / Quinns / Co-op. About €90 and will be enough for several applications of a large area.

JK probably should be treated by specialist contractors, however with an intelligent approach and awareness of all the issues a self help approach would probably be better than none at all. Specialist contractors are expensive and its very doubtful the neighbour would have the ability or willingness to pay them. Since the authorities are treating the whole thing in a very hands-off kind of way - some advice but no enforcement - its hard to see how they can challenge someone trying to treat it themselves.

The biggest issue is often trying to persuade people not to cut it or dispose of it - there are some very stubborn people who won't be guided.

Can the Department of Agriculture do anything?

Dont know where you are but most councils have a not on it

Is Japanese knotweed a regulated species in Ireland? Yes, under Regulation 49(2) any person who plants, disperses, allows or causes to disperse, spreads or otherwise causes to grow Japanese knotweed or any of the other invasive plants listed in the 2 Version 1.0, released August, 2016 Third Schedule of the European Communities (Birds and Natural Habitats) Regulations, 2011 (S.I. No. 477 of 2011) shall be guilty of an offence. Furthermore, Sections 52(7) and (8) of the Wildlife Act, 1976, as amended,1 make it an offence to plant or otherwise cause to grow in a wild state exotic species of plants.

I have Japanese knotweed on my land, do I have to get rid of it? Yes, you should take action to control and eradicate this plant from your site. By doing nothing it could be considered an offence by ‘allowing’ it to be dispersed or spread. It also makes sense to try and control and eradicate the plant from the site sooner rather than later as the longer it is left to expand and spread, the more resources will be required to deal with it. Japanese knotweed is growing near my house, should I be concerned? In most instances, Japanese knotweed and the other invasive knotweeds are growing far enough away from a house for it not to be an imminent threat but one that should be dealt with before it spreads closer to your home. If you can see Japanese knotweed growing above ground and within about 10 meters of your house then you should seek expert advice on assessing the risks to your home. While the rhizomes (underground part of the plant) are said to grow out to about 7 meters horizontally and 3 meters vertically, in reality this tends to be much less. However, spread of rhizomes beyond 7 meters has been documented where an easy route such as along ducting is available. There is an infestation of Japanese knotweed on a neighbouring property and it is spreading into my land, who is responsible to get rid of it? The landowner is responsible to ensure that they are not causing or allowing it to be dispersed or spread and should take action to control it. It is an offence for anyone to cause or allow it to be dispersed or spread2 . 

from waterford coco

https://www.waterfordcouncil.ie/media/environment/JapaneseKnotweed_FAQ_24082016.pdf

Well at least a few years ago a friend of mine worked for a company that was contracted by a council to eradicate knotweed, including from private property. That may have changed but that was the process at the time - ring the council and they'd send someone to eradicate it from your property.