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An investigation of natural London Clay is reported involving advanced triaxial, hollow cylinder apparatus (HCA) and dynamic testing techniques. Significant anisotropy was revealed at all scales of deformation, and the framework of cross-anisotropic elasticity was found to apply broadly to the initial elastic behaviour. The stiffness parameters obtained by independent techniques generally exhibited good agreement, with the greatest deviation being seen in the Poisson's ratios, which fell far from the values usually assumed in conventional foundation analysis. Probing tests established the limits to the elastic domain over a range of depths, showing that these scaled in proportion to the mean effective stress level, as did those of a second kinematic surface that surrounded the elastic domain. Once engaged, this second surface signified a new pattern of strain increment directions, faster elastic-plastic stiffness decay with strain, and also a greater dependence of behaviour on recent stress history. However, the two kinematic surfaces cover a relatively small proportion of the admissible stress space, and behaviour at larger strains is both anisotropic and strongly non-linear, features that affect profoundly the soil displacements induced by geotechnical construction in this deposit.