The barsets were made by Lassman & Co of London. See the following link for a summary of the history.
http://paperweights.com/lassman.htmTo the best of my knowledge, the double jiggers were not sold separately. Lassman purchased the handles from Pirelli, so makes sense that Pirelli also offered sets through their catalog as Frank has established.
I've had correspondence from two members of the Lassman family stating that no metal components were sold to Dunlop or Pirelli, but they may have sold complete sets or assembled barware. They also confirmed a stock of the "silk-lined" boxes for items sold separately and in sets. I am also pursuing a new lead which may yield additional information. Interestingly, the barware items stayed in the Lassman catalog at least 1981, although no new handles were purchased after 1975 or earlier.
I've owned a few complete sets, including one plated with gold. All of the sets have fixed locations for the various components. I also have had some boxed individual items with just a bottle opener, corkscrew, or a mechanical corkscrew. The non-mechanical corkscrews and bottle openers were in the same type of box and it is clear that the can opener could have been sold it the same way. Maybe even the two piece pourer was also sold this way. The spoon or double jigger wouldn't fit in one of these boxes.

Finally, there are two different sizes of spoons, only one of which would fit in the set with the case. The other spoon is longer.
Let me know if you would like any other information.
Allan