It must belong to one house or the other surely? Why would the council install a light in a privately owned alleyway? I live in a terraced house with mine and my neighbour's front doors opposite one another halfway down the alley - is that the setup you mean? Our alley is jointly owned, each owning up to the midline down the full length on the ground, with flying freehold for the bits that overhang (next door at the front, me at the back).
There's a security sensor light in the alley because I got my electrician to install it, it runs off my electricity and the switch for it is in my house. The light is installed in the alley ceiling outside both our front doors, where I own the overhanging bit so the wiring runs under the floorboards of my upstairs cupboard.
The house next door was empty when I bought mine so I just got on with getting it installed, my neighbour who's moved in since then probably has no idea who's responsible for the light now that I think about it!
The wiring for this light must go somewhere, can you follow the wiring? If it's invisible when you look at the light fitting then the likelihood is that it goes in through the wall behind, so if it's on the wall of their house then the best guess is that it's running off their electricity supply and therefore their light?
As pp's have said though, it's pretty unlikely the deeds state that anyone is required to maintain a functioning light, so even if it is your neighbour's, if they're not bothered then you can't force them or their landlord to fix it.