First check that who is the owner of files. If it is user different with www-data
you should change it to that user by doing:
$ cd /var/www && chown -R www-data:www-data html
This will take all files and change its owner and owner group to www-data
.
That's maybe not intuitive, but during Drupal installation you should do some manual work. The error you receive clearly states what you should do.
First confirm that you have directory /var/www/html/drupal/sites/default/files
. If doesn't exist you should create it by doing:
$ mkdir /var/www/html/drupal/sites/default/files
Secondly copy settings template to another file by doing:
$ cp /var/www/html/drupal/sites/default/default.settings.php /var/www/html/drupal/sites/default/settings.php
This should be pretty much enough. If there will be any further error messages. Simply follow what they ask you to do...