First is depends on what agreement or employee rule they have.

If it state company facilities Not for personal use, then you have to follow the rules.

Actually, not receiving the items should be good enough, some cases, employees have been called in for a short inquiry or if still persist, a domestic Inquiry.

But to prevent a knee jerk effect, all employees should have been notified at least a week or two that the rule is getting reinforce soon that no personal mails can be send to the receptionist, guard etc.

My previous company also did like that, no one dares to receive the stuff to office oledi unless its related to work. Even personal mail like Credit Card statements, bills etc also cannot

I'm sure they will reinforce the ruling on company mails and telephones as well.