The accuracy of several local and non-local van der Waals (vdW) corrected exchange correlation functionals on the description of the effect of pressure on ice has been investigated. In a preliminary survey, the non-local vdW correction used in conjunction with the optPBE functional was shown to provide the best overall agreement on the structural parameters of ice Ih with experiments. More importantly, this combination reproduced correctly the recently observed crystal → crystal transformation in ice Ih at 80 K prior to amorphisation. The predicted transition pressure of 1.9 GPa is somewhat higher, showing that the current generation of vdW functionals are still not sufficiently accurate for the ice system. The existence of an intermediate crystalline state with a shear-hexagonal structure confirms the earlier prediction that the collapse of crystalline structure under compression originates from the softening of phonon modes in ice Ih’s basal plane.