After further thought, I’ve realised what the problem probably was, and it’s not a permissions issue. Deleting no longer required files / folders (such as “modules_v3/menu_calendar/”) only happens when you visit the administration pages.
There are no special requirements if you are upgrading from any version later than 3.0.0. but you are likely to find initially that you have no menus displayed. To fix this login (if necessary set your browser URL to your-domain/login.php to do this), and visit the administration pages. Just visiting there is sufficient to complete the upgrade process and allow the menus to display normally again.