THe Let's Go Book mentions 2 places to stay at in Capri. I couldn't find much info on the second but I linked the website to the first. Doesn't look like a Hut though :/
Bussola di Hermes
V. Travesa La Vigna 14, in Anacapri
83 82 010
V. Campo di Teste 2, housed in Villa Margherita
83 70 230
Not much I could find online about the 2nd one, but the Let's Go book says it's a more convenient access to the beach.
Good Luck! hope you find the hut!