The paper describes the anisotropic undrained stiffness behaviour of four medium-plasticity heavily overconsolidated UK stiff marine clays as revealed through Hollow Cylinder testing. The experiments contributed to two broader studies on stiff-to-hard London, Gault, Kimmeridge, and Oxford clay strata. They involved static and dynamic testing of multiple high quality natural specimens sampled at similar depths from inland sites. This paper explores the directional dependency of the clays’ highly non-linear undrained stiffness characteristics. New data-analysis approaches are outlined that allow the stiffnesses associated with one dimensional vertical, horizontal or pure horizontal shear modes to be isolated in complex undrained stress paths. In the presented experiments, loading progressed from in-situ stresses to reach ultimate failure at a range of final major principal stress orientation angles α (defined in the vertical plane) while keeping fixed values of the intermediate principal stress ratio, b. The tests reveal strong undrained stiffness anisotropy that can impact significantly on the prediction and understanding of ground deformation patterns in numerous geotechnical engineering applications.