Aims. We investigate the impact of optically thick clumping on spectroscopic stellar wind diagnostics in O supergiants and constrain wind parameters associated with porosity in velocity space. This is the first time the effects of optically thick clumping have been investigated for a sample of massive hot stars, using models which include a full optically thick clumping description. Methods. We re-analyse existing spectroscopic observations of a sample of eight O supergiants previously analysed with the non-local-thermodynamic-equilibrium (NLTE) atmosphere code CMFGEN. Using a genetic algorithm wrapper around the NLTE atmosphere code FASTWIND we obtain simultaneous fits to optical and ultraviolet spectra and determine photospheric properties, chemical surface abundances and wind properties. Results. We provide empirical constraints on a number of wind parameters including the clumping factors, mass-loss rates and terminal wind velocities. Additionally, we establish the first systematic empirical constraints on velocity filling factors and interclump densities. These are parameters that describe clump distribution in velocity-space and density of the interclump medium in physical-space, respectively. We observe a mass-loss rate reduction of a factor of 3.6 compared to theoretical predictions from Vink et al. (2020, A&A, 362, 295) and mass-loss rates within a factor 1.4 of theoretical predictions from Björklund et al. (2021, A&A, 648, A36). Conclusions. We confirm that including optically thick clumping allows simultaneous fitting of optical recombination lines and ultraviolet resonance lines, including the unsaturated ultraviolet phosphorus lines (P V λλ1118–1128), without reducing the phosphorus abundance. We find that, on average, half of the wind velocity field is covered by dense clumps. We also find that these clumps are 25 times denser than the average wind, and that the interclump medium is 3–10 times less dense than the mean wind. The former result agrees well with theoretical predictions, the latter suggests that lateral filling-in of radially compressed gas might be critical for setting the scale of the rarefied interclump matter.