The first part of your post refers to criminal damage, which (unsurprisingly) is a criminal offence.
However trespass, per se, is not a criminal offence. If you were to leave your door open, I have every right to walk in search through all of your personal possessions and to read through all of your private documents. As far as criminal law is concerned, I would not have committed any criminal offence. (As long as there was no intent to commit theft, rape, grievous bodily harm or damage, such action would be perfectly lawful).
Climbing over a fence to enter another person's property doesn't change anything. It's still perfectly lawful. (However 'breaking and entering' is an offence).
There are specific situations whereby trespass can become a criminal offence (e.g. when it's on railway property) but it's usually only a civil matter. Even if you found me in your house, all you could do in the first instance would be to tell me to leave. If I failed to do so, and then failed to comply with a similar instruction from a senior police officer attending the scene,I could be charged with a criminal offence (but only because I refused to leave, not because of the initial trespass).
Chris