(Disclaimer - I am not a lawyer. If you want reliable legal advice, ask a lawyer!

)
As maxkatie alludes to, the
Ordnance Survey Act 1841 empowers the OS to enter any land, but only after giving written notice. For ordinary mortals, the situation is actually less clear cut than maxkatie's capital letters might wish.
Firstly, as has already been pointed out, in Scotland the right of the public to enter privately owned land against the landowner's will is enshrined in law. Such access must be transient, and there must be no "breach of the peace", but in the context of bagging trigpoints, then yes, you have full right of access.
In England and Wales, trespass to land is illegal. It's not a criminal offence so, despite the signs, trespassers cannot be prosecuted, nor even arrested by an attending police officer. However, if they cause physical damage they can later be sued for the diminution in value of the land (watch out for those crops!). If a trespasser refuses to leave when asked, the landowner can use reasonable force to eject them.
As far as I'm aware, a trespasser cannot be persued for the act of trespass itself. So, yes, the 24/7 CCTV monitoring of the historic survey station on maxkatie's property (sadly no longer containing the original pillar) would certainly be useful for proving, or disproving, any acts of physical damage. (And if there is indeed any evidence that it is T:UK users who are responsible for breaking her children's toys, then the server logs might be subpoened in any resultant court action). However, members of the public have nothing to fear from being caught trespassing on camera,
per se.
Finally please note that, in addition to any statutory obligations that may apply, the
Terms of Use of the TrigpointingUK website explicitly require all users to seek permission before entering private land.