Orbifold Hurwitz numbers and Eynard-Orantin invariants

We prove that a generalisation of simple Hurwitz numbers due to Johnson, Pandharipande and Tseng satisfies the topological recursion of Eynard and Orantin. This generalises the Bouchard-Mariño conjecture and places Hurwitz-Hodge integrals, which arise in the Gromov-Witten theory of target curves with orbifold structure, in the context of the Eynard-Orantin topological recursion.