Unread email in Deleted Items - RIPA?

I think there are two important points. One has already been raised that this is not a covert investigation so RIPA is unlikely to apply.

The second is that there is no interception of the communication, it has arrived at its destination.

The analogy is the delivery of the letter. If you are executing a search warrant and speak to the postman outside and ask for any mail for that address then the communication is intercepted. Once it is through the letterbox then it is OK to open the envelope to examine the contents (dependent on what the warrant specifies you can search for). It is not neccessary to wait for the communication to opened/read by the named addressee.