2kids2dogsnosense hehe...
Judt to clarify, I'm not saying force them to commit a criminal offence, (they choose whether they dump bins on OP's property or not), but to make ir so that IF they continue it becomes an actionable criminal offence.
OP doesnt want them trespassing & dumping on her land, neither of which will be dealt with by police as are civil matters. I've merely
suggested she plants (cheaply as per my last post) & puts sign up so that it becomes criminal if they continue. Then neighbours will either
- stop using her land- job done.
-Or if they continue, they will have caused criminal to her property (plants)....
...*
*... Which can be reported to police.
And also if you have proof (photos of perp doing it!) It is an easy 'caution' & solved crime for police. Even if police do nothing, they'll have spoken to Perp.
The neighbours who did it can't claim any high moral ground anymore as they are no.longer "tidying up the street at your expense", but are a criminal that caused damage to your property ...
Even if you don't see who did it and don't know, you're onto a winner... As you can legitimately put leaflets through all neighbours doors saying someone keeps causing criminal damage to our property at the back, at house no...., if they see anyone or if they know who it is, please contact PC Blogs at Brown street police station crime reference no. 040916123 to help with their enquiries.
(Bet all the neighbours find out who is moving their bin to yours and make sure they stop them!)
And there's always small class court espec if you have crime ref no. & get photos...
It might be worth the few pounds to chuckle over and for OP to think she could do something if she wanted to go to the trouble... 
I get on really well with all my neighbours BTW...!! And would talk to them if they did this, but OPs don't sound nice at all.