I have worked it out.
My WordPress installation was done by Install4free, and I hadn’t realised that the database had been given a prefix. I edited the wp-config.php file so that under the text that reads “// You can have multiple installations in one database if you give each a unique prefix” the prefix was properly included.
Phew! That got the adrenalin going for a while there…
Thanks Microjoes.
Re the wp-content folder, I was following the advice to “upload only those WordPress files that are new or changed to your new wp-content folder. Overwrite any old versions of default plugins with the new ones.”
The only one that looked to me like it had changed was the index.php which I did overwrite.
So not sure if that is the explanation…??