High magnetic fields in neutron stars, B~10^11^-10^13^G, substantially modify the properties of atoms and their interaction with radiation. In particular, the photoionization cross section becomes anisotropic and polarization dependent, being strongly reduced when the radiation is polarized perpendicular to the field. In a number of previous works based on the adiabatic approximation the conclusion was drawn that this transverse cross section vanishes for frequencies ω smaller than the electron cyclotron frequency ω_c_=eB/(m_e_c). In other works (which employed a different form of the interaction operator) appreciable finite values were obtained, ~σ_0gamma^-1^ near the photoionization threshold, where σ_0_ is the cross section without magnetic field, and γ=B/(2.35x10^9^G). Since it is the transverse cross section which determines the properties of radiation emitted from neutron star atmospheres, an adequate interpretation of the neutron star thermal-like radiation requires a resolution of this controversy. In the present work we calculate the atomic wave functions for both discrete and continuum states by solving the coupled channel equations allowing the admixture between different Landau levels, which provides much higher accuracy than the adiabatic approximation. This enables us to resolve the above contradiction in favour of the finite transverse cross sections at ω<ω_c_. Moreover, for any form of the interaction operator the non-adiabatic corrections appear to be substantial for frequencies ω> 0.3ω_c_. The non-adiabatic treatment of the continuum includes coupling between closed and open channels, which leads to the autoionization of quasi-bound energy levels associated with the electron cyclotron (Landau) excitations and gives rise to Beutler-Fano resonances of the photoionization cross section. We calculate the autoionization widths of these quasi-bound levels and compare them with the radiative widths. The correlation of the open channels is responsible for the modification of the cross section above the Landau thresholds. The results are important for investigations of the radiation emergent from the surface layers of neutron stars.