A new method of evaluating the Kerr constant in liquid crystals (LCs) is used to determine the temperature dependence of the Kerr effect in blue phases I and II (BPI and BPII) and to investigate the Kerr constant of the isotropic dark conglomerate (DC) phase. This method employs relatively small driving voltages and a vertical field switching (VFS) device geometry. An unusually large Kerr constant, K, is determined in the BPs of a non-polymer-stabilised material, 3×10−9 mV−2 (BPI). The large value of K is attributed to significant pre-transitional values of the dielectric anisotropy and birefringence. K follows an inverse dependence on temperature and we consequently suggest that BPI demonstrates properties best suited to electro-optic devices. The new methodology has the advantage of revealing the dispersion of K in a single measurement. It is also possible to deconvolute the influence of the Kerr effect from measurements of electrostriction of the BP lattice. Finally, the Kerr effect has been measured for the first time in the DC phase of an oxadiazole bent-core liquid crystalline material, and is found to take rather low values, 1×10−11 mV−2, which can be understood in the context of the physical properties of the material.