Bit difficult to tell exactly Andy, in the brief clip, but I think it might be either a map, or notes, resting on the turret basket. The gun itself can be seen moving up and down slightly, and the gunner appears to be looking down and to his right. The map or notes, if that is what the 'object' is, appears to be on a clipboard or something similar.
I believe gunners in the Beaufort (and Blenheim) also acted as back-up navigator, so that's possibly what's been shown. (unless he's reading a book!)