First, the upgrade to owncloud 8 in the web GUI failed. Then, I performed the upgrade in the console like this:

sudo -u www-data php /var/www/owncloud/occ upgrade

This gave an error like this (I don’t remember exactly):

An exception occurred while executing 'INSERT INTO "oc_filecache" ... Integrity constraint violation: key s_storage_path_hash is not unique
...
Upgrade failed

This owncloud is using a MySQL DB.

So what in the end solved the problem: First put Owncloud in maintainance mode:

sudo -u www-data php /var/www/owncloud/occ maintenance:mode --on

Then make sure no occ processes of old upgrade attempts are running. If there are, kill them. Then clear the oc_filecache using this MySQL command:

TRUNCATE oc_filecache;

Don’t worry, it will populate itself again during the upgrade. Then restart the upgrade:

sudo -u www-data php /var/www/owncloud/occ upgrade

This might take a lot of time! Better run this on a screen (see screen tutorial if you don’t know how) so it does not stop when your SSH connection breaks.