The Wildlife and Countryside Act 1981 lists nearly 40 non-native invasive plants. They must not be planted in gardens or caused to grow in the wild.
Other laws briefly stated in this post cover tall hedges and property damages.
The Anti-social Behaviour Act, 2003, covers tall hedges but it does not cover garden plant invasion.
The Anti-social Behaviour, Crime and Policing Act, 2014 enables local authorities and police to issue community protection notices where plants cause damage to neighbours’ gardens and properties.
The protection notice can be issued when it is shown beyond doubt that the individual in question has persistently acted in a way that has a detrimental effect on the quality of life of those around them.
Is bamboo legal to grow in the UK?
Not all bamboo plants are invasive
Running bamboo options
Choose the clump-forming bamboo, Black Bamboo, Scottish Bamboo or Phyllostachys aurea.
These bamboo plants have attractive stems and evergreen foliage.
They are good for privacy screening.
Use root barriers to grow running bamboo
Running bamboo rhizomes have the potential to damage built-up areas and cross garden boundaries.
Grow bamboo plants in barriers. This is the best way to grow bamboo screens and hedges
Here are some ideas for bamboo root/rhizome barriers when growing running bamboo.