The best solution is to co-operate with the neighbouring landowner and co-ordinate your control efforts, by sharing costs or labour, for instance.
If this solution is not effective, other courses of action can be taken:
The Environmental Protection Act 1990 provides some legal support if Japanese Knotweed is causing a nuisance to private property. A solicitor or the Citizens Advice Bureau will be able to offer advice on how to take private nuisance action against a landowner where negotiations on control or eradication have failed.
The government has reformed the Anti-social Behaviour, Crime and Policing Act 2014. Whilst this does not explicitly refer to Japanese Knotweed, frontline professionals can stop or prevent any behaviour that is deemed to be acting unreasonably and which persistently or continually has a detrimental effect on the quality of life of those in the locality. Community Protection Notices can be served against these individuals, which may require someone to control or prevent the growth of Japanese Knotweed. Local authorities and the police have the power to issue notices for invasive non-native species like Japanese Knotweed.