If you purchase and erect a fence on your land, it is your property and as such you are entitled to expect it to be respected as such. Any alterations made by a neighbour to that fence or support structure without your permission can amount to criminal damage.
Criminal damage is when a person, without lawful excuse destroys or damages any property belonging to another intending to destroy or damage any such property or being reckless as to whether any such property would be destroyed or damaged shall be guilty of an offence.
The authorities show that the term "damage" for the purpose of this provision, should be widely interpreted so as to conclude not only permanent or temporary physical harm, but also permanent or temporary impairment of value or usefulness.
For instance, lashing a tree to the fence, which then causes warping to the structure would be an impairment of both its value and usefulness.
"Postdog: I was cautioned because I had the temerity to bang a nail in a fence and use string to hold my tree straight."
- And rightly so. By banging a nail into the fence you had damaged it, by leashing a tree to it, you were subjecting the fence to stresses that it was not expected by the owner to endure. Your actions were disrespectful (not seeking permission to use your neighbour's property in such a way).