That does look like your stopcock, the pipe that joins up to it from that floor looks like a lead main, can't guarantee it is without a walk around your house, but from the photo it does look extremely likely.
However I'd be very concerned about using it knowing that the street level one is inaccessible, if it starts leaking (something that can happen when they've not been used in a long time) or breaks you'll be in some trouble. The fact they've sawn off the handle is also not going to make your life easy! If there's no way that they council will sort things out quickly enough for you, I'd make sure to have a replacement stopcock and a pipe freezing kit readily available, just in case.