Ken, I just had a look for that log file but it is completely empty though it is timestamped with the time of the attempted backup. However,, I think you have given me a good clue as to what might have gone wrong. The moodle data directory does indeed have www-data (the apache user) being able to read and write, but I now have a very bad feeling that somewhere along the line while moving the moodle data directory I might have manually deleted something inside it or pointed it accidentally to a different moodle data directory. Perhaps, moodle is now trying to write or read something from there that no longer exists? Hence the "Can not read file, either file does not exist or there are permission problems" error.
Do you have any idea how I can effectively "reset" the moodle data directory? Effectively, on this particularly course, I am not really using moodle data for uploads, images, folders etc. but obviously it is being used for cache and backups etc. My question is what happens on an open moodle install if I completely wipe everything out of moodle data, and leave a nice clean empty directory which apache has access to? Does moodle effectively start rebuilding moodle data as it needs to?