Ptychographic X-ray computed tomography is a phase-contrast imaging technique capable of retrieving three-dimensional maps of the index of refraction of the imaged volumes with nanometric resolution. Despite its unmatched reach, its application remains prerogative of a limited number of laboratories at synchrotron sources. We present a detailed description of an experimental procedure and a data analysis pipeline which can be both exploited for ptychographic X-ray computed tomography experiments at any high-brilliance X-ray source. These have been validated at the I13-1 Coherence Branchline within the first experiment of its kind to be successfully carried out on a biological sample at Diamond Light Source.