We performed Rapid-Response Mode (RRM) VLT/UVES high-resolution UV/ optical spectroscopy of the GRB 080310 afterglow, starting 13 min after the burst trigger, in order to investigate the ISM in the GRB host galaxy. The four spectra show remarkable features at zGRB, including a low log N(H i) = 18.7 and time-variable absorption from ground-state and excited levels of Fe ii and Fe iii, the latter being observed for the first time in a GRB afterglow. These observations indicate i) ongoing photo-ionization of the surrounding gas due to the GRB radiation and ii) Fe and Cr overabundances in the host galaxy ISM. We derive ionic column densities through a four-component Voigt-profile fit of the absorption lines and investigate the pre-burst ionization level of the gas with CLOUDY photo-ionization modelling. The resulting intrinsic [Si/Fe] = −1.4 ([C/H] = −1.3, [O/H] < −0.8, [Si/H] = −1.2, [Cr/H] = +0.7 and [Fe/H] = +0.2) for the whole line profile - and even more extreme for one of the absorption components - cannot be explained with current models of SN yields. Dust destruction may contribute to the marked iron overabundance, possibly induced by the burst. The overall high iron enhancement along the line-of-sight also suggests little recent star formation in the host galaxy.