Just been searching Jstor for "Children's Mobile Library" and "Bookmobile", but got few results. the only relevant thing was two sentences in a 1947 article about a library authority in America, that sent out their book mobiles to take books tho increase the literacy in sparsely populated areas. This sounds a bit vague, but I did save the page.
Also tried to make contact with someone called Ian Stringer who acoring to Cilip is Britain's foremost authority on Mobile Libraries. I hope he replies.