Of course we can investigate your work emails and internet activity. .We need to be able to do that to investigate accusations of misconduct. But as an employee you've been told that can happen, and are reminded every time you log in and you've been told to avoid using your work email for personal use for that very reason.
As someone who regularly carries out these investigation I'd also add that the evidence I've gather through instigating has proved innocence far more often than it has proved guilt.
The ability to investigate is not live monitoring since that would fall foul of RIPA/RIPSA.
I think there is a bit of confusion over active monitoring and having logs to enable investigation.
But please, pretty please don't use your work email for personal shit. I don't want to know about any more married men hiding in the closet arranging liaisons with boyfriends, or who is humping whom in the office, or the the plans for your next coke fuelled party.