Jimmie
It's still fairly unusual to find individual stopcocks for tenement flats. When they were built the cold supply from the street runs under the close floor, branches into two and then runs up the kitchen wall to the attic. Each kitchen had a cold tap fed fron this, the attic cistern was typically built from 6" by 3" timber half lapped at the joints and then lead lined, about a 1000 gallons. A supply from this went down the building, each flat tapping off for bathroom cold and hot water cold feed, which is part of the reason why bathrooms were often at the front of buildings. What's the betting that your daughters bathroom is long and thin, and not really big enough for a bath.
I have been to one or two tenements where this cistern arrangement was still in use, but I wouldn't want to live under a 1000 gallons of water contained in a 130 or so year old tank. Didn't really want to go in the attic either, feet deep in pigeon guano at best. More recently when lead pipe removal attracted grants, flats were often repiped and everything connected to mains water, but a lot depended on the factors inclination. Your picture is most definitely not the stopcock but is the remains of a mechanical door bell.
Regards
Martin (in Glasgow)