'Airey' is a London child's pronunciation of 'area'. In the days when ball games could still be played in the street - and where the street happened to be one with houses with basements (as many in the East End were, before the Blitz) - a ball that went 'down the airey' had to be retrieved by opening the gate and going down the narrow steps, risking the wrath of the occupants.

MtheGM's version was the usual form when I was a child in the 1930s, but I don't hear it much now. The aireys have nearly all gone and so have the safe, car-free streets in which children's games could be played.