According to my book, Arley and Arley-Barley comes from Sir Gawain and the Green Knight, written in the 14th century.
At the beginning of the poem the gigantic green stranger at King Arthur's court challenges any man to strike him with an axe "so long as I shall have leave to launch a return Barlay". Here, the word "Barlay" means free or unchecked, and it's not hard to see how, it came used by West Midlands kids in their play when wanting a break. Children shouted "Barley" or "Arley-Barley" when playing tig.