Motivated by all the new info, I cleaned up one of the later? taps, which has both "C.M.C." and Enots brands, plus the patent number above. What a lovely object, and much more interesting than the usually-seen repros. Also it has the correct number of hexagons!
The tin I'm delving into had quite a few taps, and I can make a few observations. Almost all of the taps were nickel plated, with only one chrome plated, and a couple in plain brass. The brass ones are old (1950s) no-name brand, so probably just cheap parts originally. Some taps are unbranded, some have the CMC brand, some the brand and the patent number, and some like the one in the photos with Enots, CMC and the patent number.
As 33d6 commented earlier, the name "concentric" was used to describe these taps, and in the 1924 Show number (for the 1925 season) Best and Lloyd exhibited concentric taps, with round ends. It looks like all the concentric taps were licensed under the patent GB194036 at they are all much the same, with variations only in the detail of the pushers.
Anyway, thanks everyone as it's nice to learn something about which I had no ideas at all two days ago.
Cheers
Leon