Alie, all my sympathy, what a difficult situation you are in. I had always assumed from the state of the house and garden that you were dealing with an elderly couple no longer coping. I wonder why they bought a house, they sound as if they are more suited to flat living.
Could you afford a consultation with a specialist property lawyer to find out what your options are?
DD is in an ex-council house and the next door house, once occupied by a pleasant elderly woman is now occupied by a problem family, who, similarly, completely neglect the garden. The Council are very good over this, when neighbours complain about the state of the garden or build -up of rubbishe the tenants get threatened with eviction if they do not tidy up the outside and get rid of the rubbish
However, at one point she was affected by the smell of cigarette smoke coming into her house from her neighbours. The council were very unhelpful about this and in the end after much thought she took up bedroom floorboards alongside the party wall and sprayed about six inches of builders foam all along the wall where the joists went into the wall, then replaced the floor boards and that does seem to have solved that problem.