I feel sure I must be missing something obvious because I would imagine there are tens if not hundreds of thousands of JabRef users using Harvard referencing style.
I do understand I can make my own .jstyle file (which is probably not as bad as it sounds, because I should imagine I can modify the default one) but what am I missing please…
Unfortunately, I do not think that you have missed anything. There are probably style files out there, but none that have been contributed to the repository (there are very few that have been contributed).
I had a look at exactly this topic some while ago. The problem is that there is no official Harvard style. “Harvard” seems to be a rather generic term that covers the author-year style of citation. There are properly defined author-year styles like APA. A number of university libraries post Harvard style guides for students but they are all slightly different.