Delving back through the mists of time, RN slang for helicopter was definitely Paraffin Pigeon pre 1970's. Google reference shows Jackspeak to be paraffin pigeon, so I would surmise that the morphing into Budgie sometime in the 80's may have been an RAF move.
Since North Sea references also tend toward P.Pigeon, and early NS crewing was predominantly ex RN, I would suggest that somewhere this got bastardised into P.Budgie and remains a term mainly used by UK Mil and in areas influenced by ex UK Mil aircrew.
We also used to refer to the jet jockey's mounts as aluminium death tubes, just to go a little bit OT
