You must have safe means of escape from your second floor. Your options are limited. The preferred route is via a protected stairway to a ground floor exit. That's what has been proposed - the partition across the hallway protects the whole stairway. As an alternative it is sometimes acceptable to escape from second to first floor and out of first floor windows. That can be done if the first floor windows comply with escape window criteria and the route from second to first floor is protected. Unfortunately your staircase is not protected and I can't see an easy way to make it so without considerable knocking around of the first floor landing and losing a bit of bedroom 2. A sprinkler system can be an option in the right circumstances but they are only really viable to install when you are stripping a building back to the bones. So I think your only viable option is the ground floor partition.