I am not a lawyer, and I'm not the one making the call for my clients on any potentially legal matters. Would appreciate to hear the thoughts of those with experience in this area.
My gut feeling is that, although users may have signed T&Cs allowing this, UK/EU courts would hold that there is a reasonable expectation of privacy around the mailbox, and so the Regulation Of Investigatory Powers Act 2000 (RIPA) would apply . This means that such a host couldn't go digging themselves into the email.
However, a potential route in could be via getting the source to make a subject access request under the Data Protection Act 2000 (DPA) into the organisation, supplying their external email address, in response to which there would be a very tenuous grounds to release the mail. However:
1. I'm fairly sure that this would be considered a misreading of the DPA, and hosted mail would be considered information held by the client, rather than the host
2. There's such an obvious claim here that all of this would have happened under duress, and that's a huge can of worms....
So in conclusion, I suspect the only way to legally get at such an email within the UK/EU would be via working with law enforcement, or via one of the two parties to the discussion providing it.
 Most of the relevant acts of UK law are descended from common EU legislation, and apply broadly across the EU, hence the repeated use of UK/EU here
 Unless you're working in certain very strict offices with clear Security Operating Procedures (SyOPS) and regular training, UK/EU courts are likely rule that even corporate email systems can be considered to hold personal communications protected under RIPA