  We prove that a generalisation of simple Hurwitz numbers due to Johnson,
Pandharipande and Tseng satisfy the topological recursion of Eynard and
Orantin. This generalises the Bouchard-Marino 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.
