OK, I will stand corrected here, but, if a wild/feral bird/animal is not named on the schedule list of quarry/vermin species then it legally cannot be shot. You can only legally shoot quarry species and vermin as per the statutes.
However, on the flip side, the peacock will not be protected, per se, and there is nothing to stop a person catching one in a cage trap/feeder trap and killing it. However, the peacock may belong to someone so then you'd have to hand it back over to them or it could be construed as theft.
It is a grey area of the law and, I believe it would pivot on location of