Photon quality correction factors (kQy) for ionization chamber photon dosimetry in an epithermal neutron beam were determined according to a modified absorbed dose to water formalism which was extended to mixed radiation fields. We have studied two commercially available ionization chambers in the epithermal neutron beam optimized for BNCT at the facility at Studsvik, Sweden. One of the chambers is nominally neutron insensitive; a magnesium-walled detector flushed with pure argon gas (denoted by Mg/Ar). The second chamber has approximately the same sensitivity for neutrons and photons; it is considered a 'tissue equivalent' detector, with A-150 walls flushed with methane-based tissue-equivalent gas (denoted by TE/TE). The kQy-factors in epithermal neutron beams have previously been assumed to be equal to unity or estimated from measurements in clinical accelerator produced photon beams. In this work the kQy-factors have been determined from absorbed dose calculations using cavity theory together with Monte Carlo derived electron fluences obtained with the MCNP4c system for water and PMMA phantoms. The calculated quality correction factors differ substantially from unity, being in the order of 10% for the Mg/Ar detector at shallow phantom depths, and between 2 and 4% for other depths and for the TE/TE chamber.