The shear strength of heavily overconsolidated, stiff-to-hard plastic clays is crucial to their stability and also influential on the ground movements they develop in many geotechnical engineering applications. This paper considers the shear strength anisotropy of the London, Gault, Kimmeridge and Oxford clays through advanced hollow cylinder experiments on multiple high-quality samples taken at similar depths from inland sites where the geotechnical profiles have been established by comprehensive laboratory and in situ testing. Suites of undrained tests are reported, which loaded specimens from their in situ stress states to reach ultimate failure at pre-defined final major principal stress axis orientations defined in the vertical plane, while also controlling or monitoring the intermediate principal stress ratio, b. Both stress path and simple shear tests were undertaken with the hollow cylinder apparatus, which offers key advantages over conventional simple shear equipment. The interpretation reveals patterns of marked shear strength anisotropy that impact significantly on numerous geotechnical engineering applications.