Here's a shot of the Giller socket along with some look-a-likes in the line up. I think the consensus is that these are New Britain, but of course none of the New Britain sockets I have look like this, go figure. Here is an underlined Craftsman, the Giller, a Husky, a Mustang and two None Better sockets with a similar band.

It seems apparent Giller was a government sourcing contract brand, and the sourcing was all over the board.  Thanks for sharing.  First I've seen in that style with a Giller name.  I would agree it was New Britain production.