A series of one-dimensional incremental load consolidation–hydraulic conductivity tests was performed on reconstituted clays. Based on these tests, together with the test data compiled from the literature, the quantitative interrelation between the variation of hydraulic conductivity in the vertical direction with void ratio and the compression behaviour is established. It is found that the hydraulic conductivity in the vertical direction can be expressed as a function of void index, initial void ratio and void ratio at the liquid limit. The effects of initial void ratio and void index on hydraulic conductivity in the vertical direction for a given clay with a given void ratio at the liquid limit can be comprehensively attributed to the effect of void ratio on hydraulic conductivity in the vertical direction. These two findings introduce the point that the hydraulic conductivity in the vertical direction is a function of void ratio and void ratio at the liquid limit. Empirical equations are proposed to determine the hydraulic conductivity in the vertical direction using void ratio and void ratio at the liquid limit or using effective vertical stress, initial void ratio and void ratio at the liquid limit. These two empirical equations are correlated based on the concept of intrinsic compression.