We have measured both the ordinary and extraordinary refractive index of m-plane cuts of wurtzite ZnO, GaN, and AlN single crystals at room temperature and as a function of hydrostatic pressure up to 8 GPa. For that purpose we have developed an alternative optical interference method, called bisected-beam method, which leads, in general, to high contrast interference fringes. Its main feature, however, is to be particularly suitable for high pressure experiments with the diamond anvil cell, when the refractive index of the sample is low and similar to that of diamond and/or the pressure transmitting medium, as is the case here. For all three wide-gap materials we observe a monotonous decrease of the ordinary and extraordinary refractive indices with increasing pressure, being most pronounced for GaN, less marked for ZnO, and the smallest for AlN. The frequency dependence of the refractive indices was extrapolated to zero energy using a critical-point-plus-Lorentz-oscillator model of the ordinary and extraordinary dielectric function. In this way, we determined the variation with pressure of the electronic part (no-phonon contribution) of the static dielectric constant ε∞ . Its volume derivative, r = d ln ε∞ /d ln V , serves as single scaling coefficient for comparison with experimental and/or theoretical results for other semiconductors, regarding the pressure effects on the dielectric properties. We have obtained an ordinary/extraordinary average value r of 0.49(15) for ZnO, 1.22(9) for GaN, and 0.32(4) for AlN. With the values for the ordinary and extraordinary case being within experimental uncertainty, there is thus no apparent change in dielectric anisotropy under pressure for these wurtzite semiconductors. Results are discussed in terms of the pressure-dependent electronic band structure of the materials.