Joe Gilbart in Guns Review 1982 discussed these briefly and disclosed that they were first patented by Lanes Brothers in 1884 (British Patent 11711). John Atkins, in Airgunner, August 2014, then informs us that they were registered as Lanes Patent Shot Cartridges on April 15, 1885, and were introduced onto the market in June of that year. They were evidently made by others over the years (such as by Modarcom, as with the Star brand spread shot pellet box pictured in the original post), but it is not clear when they actually disappeared from the marketplace. I would guess some time well before the second World War.
I have ensured that the pellets have a similar weight to a typical .177 waisted lead pellet. With the chalk they have an average weight of 0.62 grams, and the inner 12 lead shot weighs about 0.58 grams. So the chalk carrier is less than 4% of the total weight.
I am going to try them in a rifled barrel, as I think the rifling might hold back the outer chalk surface of the pellet slightly while the heavier lead shot moves forward, and this will encourage complete disintegration in the barrel. Ideally one would want a choked barrel, but you can't have everything!