Strange. I looked at the timeline today and it seems to be correct for the current backups now. The diff backup is no longer shown as running continuously.
Unfortunately, all the backup history is missing for about a two week period (even from the Activity History tab) - it seems some kind of reset happened which cleaned up the problem, but also wiped out the history. At least the history still exists in the SQL Server Agent log.
I'll be interested to see if anyone else posts a similar issue but in the meantime, thanks to the viewers of this thread,