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Mamba,
I really appreciate you taking the time to look at this. It did not occur to me to check the permissions because they were previously set correctly to 777 and are so set on my live site. This test site is essentially a duplicate, although there are modules installed that I'm just testing.
I think what might have happened is this: The first time I tried to upgrade I made a mistake in the use of my FTP client (clicked the wrong button), which caused some of the files that were not being updated to be deleted. I therefore copied over all the original files from backup, then tried again. I think that the xoops_cache/caches permissions were changed in the backup file, something I didn't expect. I checked that file, which I still have, and indeed they are set to 755. So, I learned not to assume that files in a backup are set as in the originals.
Once again, thanks.
barryc