This is a subject I find interesting as I continue to study the evolution of sun helmets. One notable point that people often don't understand is that most "pith helmets" made in Europe are actually cork helmet. A pet peeve of mine is that pith and cork are so confused.
I even wrote about it on my MilitarySunHelmets.com website:
http://www.militarysunhelmets.com/2012/pith-vs-cork-not-one-and-the-same" onclick="window.open(this.href);return false;
The quick point is that cork mainly comes from Portugal and Spain (with some from Algeria, Morocco, France and Italy), and that it is a bark from a tree - whereas sola pith is a milky plant. A couple of helmet books suggest that pith is a type of cork and I even had someone arguing with me at SOS because a book on WWII German helmets makes that point. That annoyed me because -- well, it is just wrong, but to this guy if a book said it then it must be true.
Well, the other thing that is interesting is that I can't exactly understand is why these are considered an to be made of an ersatz material? Cork was in short supply during World War I, so much so that the Austrian sun helmets for its troops in Palestine and the Balkans were made of straw. That is what my Austrian WWI sun helmet is made of, and my colleague Stuart Bates has two British Wolseley helmets that are straw - most probably didn't survive and few were probably saved! But it seems that due to cork shortages straw and other materials were used.
I bring this up too because I've been working on a theory about the WWII era felt helmets. Both the Germans and British used felt sun helmets. The brown German one has always been called the "second pattern" and it has been suggested that it was never intended for Africa. I don't agree at this point because I've never seen one with a date that is earlier than 1942 except in liners that I felt were for the so-called "first pattern." The liners would fit in either helmet - trust me I've tried over the years. Also the British Wolseley helmets stopped being made of cork in late 1941 and instead felt was used. I've never seen a cork helmet from 1942 or later, until after the war when the Royal Marines used the helmets again. The exception are the Naval style Wolseley helmets made in Canada, so perhaps there was a bigger supply of cork.
Anyway, back to WWI - when were these German cork helmets issued. I have seen a couple in person. I know these have always been called "cork" helmets but is it absolutely canvas over cork? I'd really like to take a closer look now, because I guess I am wondering whether it is truly cork.
The final thing I'll add is that there were French and Belgian cork helmets made after the war for parades and the like. I think in the post-war years there was probably a glut of cork from Portugal.