Ok, so the BBC won't let me see the emails. Information held for journalistic purposes is exempt, it seems.
This isn't the end of the world though, because all I want is some confirmation that there were some emails, and if there were, when they arrived at the BBC.
I've gone back to the Beeb and asked if I can see the dates and times of email correspondence between Roger Harrabin and the WMO. Surely the dates and times of the emails isn't information held for journalistic purposes.