As I've had no response (again) and as I can't work on the site until this issue is resolved, I took the decision to delete the site and start again to see if that made a difference. I deleted the files of the site and deleted the database. I then created a brand new empty database, installed Joomla and my template, SPPB etc.
To my shock, when I went into the SPPB component, there were all the pages I had created on the old site. Clearly this suggests a browser cache issue (I'm using Chrome). I cleared the cache, logged out and back in again and the pages were still showing. I cleared the site cache and then again the browser cache, logged out and back in again but the pages still showed up.
I then logged into the site using a different browser, Safari (I'm on a Mac). Using Safari none of the pages from the previous site could be seen. Great, so it's a browser cache issue in Chrome then? Well, no. Because then I tried to create pages in Safari and even though it said the pages had been saved, they didn't appear in the list of pages in SPPB. If I then logged in using Chrome, the new pages still weren't visible. Equally if I tried to create pages in Chrome, they wouldn't be visible in the list of pages when viewed in Chrome or in Safari. So this isn't an issue with one browser, it's an issue with all browsers. So it's a site caching issue then? Well no, because if I clear the site cache it makes no difference and I've also set, in Global Config, the system cache to Off.
I've no idea what else to try!