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Your neighbour owes you a duty of care in regard to the knotweed as potentially this could cause damage to your property as well as have an affect on its market value. Not to mention the damage to the neighbours house.
You should speak to the neighbour about this and follow up with a letter, including a copy of the survey. The neighbour will have to organise for the weed to be treated when it flowers in the Spring/Summer.
If the neighbour has a mortgage, it will also be a condition of their mortgage to maintain the property.
I also found this information which
Allowing Japanese knotweed to spread onto neighbouring land could be considered either a statutory or private nuisance.
Where a local authority is satisfied that a statutory nuisance exists or is likely to occur, defined as “any premises in such a state as to be prejudicial to health or a nuisance”, it is able to serve an abatement notice imposing certain requirements under Part III of the Environmental Protection Act 1990. A prosecution, in a magistrates‟ court, may follow if the party on whom the notice has been served fails to lodge an appeal notice within 21 days.
The common law of private nuisance defines nuisance as the “unlawful interference with a person‟s use or enjoyment of land, or some right over, or in connection with it” [Read v Lyons and Co. Ltd, (1945) K.B.216]. This principle allows landowners or tenants of leasehold properties who have a right to the land affected to bring an action against the person responsible. In addition, the rule of Rylands v Fletcher (1868) re-lates to strict liability for foreseeable damage caused by escapes resulting from non natural uses of land.
Private individuals can under the Environmental Protection Act 1990 Part III, Sec-tion 82 make a complaint to a magistrates‟ court, under statutory nuisance, requesting an Order against a particular individual to abate the nuisance. Prior to applying for an Order it is necessary to write to the individual giving them notice that such an applica-tion is to be made. Individuals who have successfully obtained a nuisance order from a magistrates‟ court are entitled as of right to their costs, if the nuisance existed at the time that they initiated the proceedings.