The precise error Owncloud would give at the top of the screen when I tried to upload a file was: Upload failed. Could not find uploaded file.
I spent ages trying to fix this with nothing online to help (which is why I’m writing this now for other’s, in case others are as ignorant as I am).
Go into /etc/php/php.ini and ensure that *upload_tmp_dir* is set to a directory included in the *open_basedir* path further up the file. The *open_basedir* set of directories is a list of base directories all PHP code can interact with. If your upload directory is not in there, any uploaded files are sent in the ether and then lost – with Owncloud complaining that it ‘can’t find them’. Owncloud can’t see the directory if it’s not one of those included in *open_basedir*.