We have commenced a detailed analysis of the known sample of Galactic post-asymptotic giant branch (PAGB) objects compiled in the Toruń catalogue of Szczerba et al., and present, for the first time, homogeneously derived distance determinations for the 209 likely and 87 possible catalogued PAGB stars from that compilation. Knowing distances are essential in determining meaningful physical characteristics for these sources and this has been difficult to determine for most objects previously. The distances were determined by modelling their spectral energy distributions (SEDs) with multiple blackbody curves, and integrating under the overall fit to determine the total distance-dependent flux. This approach was undertaken for consistency as precise spectral types, needed for more detailed fitting, were unknown in the majority of cases. The SED method works because the luminosity of these central stars is very nearly constant from the tip of the AGB phase to the beginning of the white dwarf cooling track. This then enables us to use a standard-candle luminosity to estimate the SED distances. For Galactic thin-disc PAGB objects, we use three luminosity bins based on typical observational characteristics, ranging between 3500 and 12 000 L⊙. We further adopt a default luminosity of 4000 L⊙ for bulge objects and 1700 L⊙ for the thick-disc and halo objects. We have also applied the above technique to a further sample of 54 related nebulae not in the current edition of the Toruń catalogue. In a follow-up paper, we will estimate distances to the subset of RV Tauri variables using empirical period-luminosity relations, and to the R CrB stars, allowing a population comparison of these objects with the other subclasses of PAGB stars for the first time.