tibilicus, since you appear to be in England, you should check the cat for a microchip. Usually, if you feel (gently) around the scruff of the neck, you may find a nodule around five millimetres long. If it has one, it's a simple matter to take it to the local vet who will scan it and tell you the owner. Or of course, notify the RSPCA - from your description, it may have been abandoned recently (its condition getting worse) as sadly, more people are losing their jobs and thus think it is a solution to throw a cat out to rely on its own devices.