The perovskite-type (ABO3) solid solution (1-x)Na0.5Bi0.5TiO3-xBaTiO3 (NBT-xBT) is a promising alternative for currently market-leading but ecologically undesirable Pb-containing ferroelectrics. However, the properties of NBT-xBT need to be improved to meet the requirements of a suitable substitute. This can be done by tuning the local ferroic atomic clustering via additional A- or B-site doping, but a lack of clear understanding of the composition-dependent nanoscale structural features in NBT-xBT prevents from going behind the trial-and-error approach. Analysing the response of the structure to external stimuli such as temperature, pressure or electric field is the best way to address this issue. Here we report the pressure-induced structural changes in NBT-xBT single crystals with x= 0, 0.048 and 0.074. The x= 0.048 compound is of particular interest, since it corresponds to the morphotropic phase boundary, where the dielectric and piezoelectric properties are enhanced. Using the diamond-anvil-cell technique, we have performed high-pressure Raman-scattering experiments up to 10 GPa and in-house single-crystal X-ray diffraction (XRD). The Raman data show that upon pressure increase the polar order in NBT-xBT is suppressed in favour of antiferrodistortive order. The off-centred shifts of B-site Ti cations and the local-dipoles coupling between adjacent A and B sites are suppressed, while the fraction of off-centred A-site cations increases. Above a certain pressure an ordering process in the A-site sublattice occurs, as pre-existing uncorrelated A-site dipoles align to each other. Moreover, the pressure increase induces enhancement of correlated octahedral tilting modes, which, for Ba-doped compounds, are not observed at ambient pressure. The pressure dependence of the accumulated Eulerian strain derived from XRD data on Ba-doped NBT as well as the anomalous broadening in the Bragg-peaks at high pressures further reveals the evolving ordering processes, in full accordance with Raman-scattering analyses.