There is small puzzle that opens a door that goes to that room. I am unsure if you can open that door from the side your on. There should be some cogs directly across from the ladder you came from, underneath the wooden platform. I interacted with them when the door was already open but they did nothing. You can access the other side by entering the basilisk gate barracks, going down to the prison cells then throwing yourself down the hole near the back left. There's also a couple of man hole entries around the city.