Minor update, this was being caused by the definition of WP_TEMP_DIR in the wp-config.php file.
When WordPress does a plugin update, it needs a temporary location to store the files as they are downloaded. When we moved the files, this constant pointed to a non-existent location.
You can remove the constant (If it's there) or set a new one e.g.
Just make sure to update the owner and permissions for that directory.