The hospital is not featured at all in Mark Hammond's story but it is seen in Frank Carter's first mission, The Bargain Basement. After Jake shot Joe Fielding at the Bargain Basement Brothel, Frank had to drive Joe to the hospital quickly in order to save his life. As it wasn't that far, it made sense that this was the hospital Joe went to. Frank raced through the streets with a bleeding Joe but made it to the hospital in time. Joe was then taken inside and treated for his injuries. Frank then returned back to Snow Hill to question Jake. The hospital is later seen in the mission, Stalking McCormack. After learning that McCormack is corrupt and working with Charlie Jolson, Frank overhears him talking to Big Walter about the fact that this officer, DC Joe Fielding, whom Jake had shot earlier, can testify against Jake at a trial as he survived the shooting. McCormack instructs Walter to take care of the job along with some other gangsters in the Bethnal Green Mob and gives him all the information he needs. He says there are armed guards by the door and that Joe is at UCL Hospital on the 2nd floor in the intensive unit. In order to save Joe, Frank quickly leaves the depot and drives over to the hospital. On arrival, he runs upstairs and finds Joe is alive and that the attackers haven't arrived yet. Frank then speaks with Joe who informs him of McCormack's sudden and very recent death as well as some information about an old lock-up garage that belongs to Charlie, which Frank should check out. Frank prepares to leave when suddenly an armed guard is shot at outside by Big Walter. Frank exits the room Joe is in and kills the gangsters as they try and kill Joe. Big Walter flees to the floor below and Frank follows him downstairs. Frank shoots more of the attacks in different parts of the hospital and eventually either kills or arrests Big Walter, depending on the player's choice. Once all the gangsters are taken care of, Frank leaves the hospital as Joe is safe and more armed guards have arrived in the lobby of the building. Frank then leaves the hospital and heads to the lock-up. This happens in the following mission, Do the World a Favour.
In The Getaway: Black Monday, it still exists and can be entered by the player, but only the reception area. The rest of it is sealed off. It is not featured in the storyline at all however, so this can only really be done in Free Roaming mode.