I used a 100% cotton fabric from IKEA called BERTA RUTA. Not sure whether it has the same name all over the world. As far as I know IKEA names things differently depending on the region it is sold. One meter of that fabric made three big pouches and a small one, btw. For the drawstrings I simply used shoelaces.
The drawstring pouches are also mentioned in Martha Stewart's Encyclopedia of Sewing and Fabric Crafts, which I got for my birthday last year. Great book with good information and nice project ideas in it!