I have, somewhere! details of a padlock with a built in alarm that, if touched when activated sets off a shrill alarm. This would, at least, set the dogs barking and, hopefully make any intruder scarper.
I will search through the piles of papers, debris etc. that is my office/filing cabinet a.k.a. the dining table and see if I can find it.
You could, without leaving yourself open to prosecution, put up signs saying e.g. "Please ensure gate is secured, my dogs are free-ranging"
Good luck to you and bad luck to whoever is responsible!!