Not sure what spolation in the original post means, but I suppose it is ruining the monuments, right?
My two cents on the matter: I have some experience doing fieldwork in Portugal and Spain during my PhD. I was looking for amphibians, and the best place to find them is in small ponds, usually man made, intended to make potable water available for cattle or to water the crops. Most of these are in private property. In some cases, it was easy to ask someone in the vicinity who the field belonged too (usually the exact person we found, or a close relative), but in other places, there was no one to be found in a 10 km radius. In these cases, we would usually go in anyway (not that I recommend it) and explain ourselves if someone came by asking what we were doing. Depending on the height of the fence, the normal reactions would go from curiosity to threats to call the police (not that anyone did, after we explain what we were doing or left the premisses). It also helped that we had a permit from the National Nature Conservation Institute to capture the animals.
In addition, in Portugal, hunters are permitted to cross fences up to 3 meters without permission in designated hunting areas, during hunting days.
In other words, now your local legislation about trespassing, talk to local people and land owners and explain clearly what your intentions are. The national WLM pages should perhaps mention something on the lines off:
"Beware that some monuments are located in private property. Be sure to ask for permission to land owners before entering private land and taking photographs."
Gonçalo