London's original plan was to stage shooting events for the 2012 Olympics and Paralympics at Bisley in Surrey.
But concerns from the International Olympic Committee about the spread of venues from the planned Olympic village prompted a rethink.
The Royal Artillery Barracks at Woolwich in south-east London are much closer to the core zone, although they lack the existing world-class facilities of Bisley.
The buildings, which date back to 1776, and are now home to the Museum of Artillery.
London's plan is to construct a temporary indoor venue for 7,500 spectators which would be moved to another part of the UK after the Games.