  In the present paper we address double parton scattering (DPS) in quasi-real
photon-proton interactions. By using electromagntic and hadronic models of the
photon light cone wave functions, we compute the so-called effective cross
section, $\sigma_{eff}^{\gamma p}$ which allows us to calculate the DPS
contribution to these processes under dedicated assumptions. In particular, for
the four-jet photoproduction in HERA kinematics we found a sizeable DPS
contribution. We show that if the photon virtuality $Q^2$ could be measured and
thus the dependence of $\sigma_{eff}^{\gamma p}$ on such a parameter exposed,
information on the transverse distance between partons active in proton could
be extracted. To this aim, we set lower limits on the integrated luminosity
needed to observe such an effect which would allow the extraction of novel
information on the proton structure.
