“Joy-tu Boyl/Boil” is a mystery to me. The buttons were only advertised in 1947-8. They appear on cards of 12, 16 or 24 depending on the size. They are either 2 or 4 hole sew throughs in plain colours: I’ve seen pink, white, green, red maroon, brown, dark and light blue and black. Who made them? What does “No. 79512 Regd.” (on all the cards) refer to?
“Modern Miss” buttons were not , as far as I can tell, ever advertised. They were almost certainly (from the identical designs of some of the buttons) made by General Plastics in the 1940s before they adopted the ‘Beaucliare’ branding around 1951.