Context. Over its 13 yr of operation (1990–2002), the Faint Object Camera (FOC) on board the Hubble Space Telescope (HST) observed 26 individual active galactic nuclei (AGNs) in ultraviolet (UV) imaging polarimetry. However, not all of the observations have been reduced and analyzed or set within a standardized framework. Aims. We plan to reduce and analyze the AGN observations that have been neglected in the FOC archives using a consistent, novel, and open-access reduction pipeline of our own. We then extend the method to the full AGN sample, thus leading to potential discoveries in the near future. Methods. We developed a new pipeline in Python that will be able to reduce all the FOC observations in imaging polarimetry in a homogeneous way. Most of the previously published reduced observations are dispersed throughout the literature, with the range of different analyses and approaches making it difficult to fully interpret the FOC AGN sample. By standardizing the method, we have enabled a coherent comparison among the different observational sets. Results. In this first paper of a series exploring the full HST/FOC AGN sample, we present an exhaustively detailed account of how to properly reduce the observational data. Current progress in cross-correlation functions, convolution kernels, and a sophisticated merging and smoothing of the various polarization filter images, together with precise propagation of errors, has provided state-of-the-art UV polarimetric maps. We compare our new maps to the benchmark AGN case of NGC 1068 and successfully reproduce the main results previously published, while pushing the polarimetric exploration of this AGN futher, thanks to a finer resolution and a higher signal-to-noise ratio (S/N) than previously reported. We also present, for the first time, an optical polarimetric map of the radio-loud AGN IC 5063 and we examine the complex interactions between the AGN outflows and the surrounding interstellar medium (ISM). Conclusions. Thanks to our newly and standardized reduction pipeline, we were able to explore the full HST/FOC AGN sample, starting with observations that had not been previously published (e.g., IC 5063 here). This pipeline will allow us to make a complete atlas of UV polarimetric images of the 26 unique AGNs observed by the FOC, highlighting the importance and necessity of (imaging) polarimeters for the upcoming new generation of 30-m class telescopes.