We used high hydrostatic pressure to perform photoluminescence measurements on polar ZnO/ZnMgO quantum well structures. Our structure oriented along the c-direction (polar direction) was grown by plasma-assisted molecular beam epitaxy on a-plane sapphire. Due to the intrinsic electric field, which exists in polar wurtzite structure at ambient pressure, we observed a red shift of the emission related to the quantum-confined Stark effect. In the high hydrostatic pressure experiment, we observed a strong decrease of the quantum well pressure coefficients with increased thickness of the quantum wells. Generally, a narrower quantum well gave a higher pressure coefficient, closer to the band-gap pressure coefficient of bulk material 20 meV/GPa for ZnO, while for wider quantum wells it is much lower. We observed a pressure coefficient of 19.4 meV/GPa for a 1.5 nm quantum well, while for an 8 nm quantum well the pressure coefficient was equal to 8.9 meV/GPa only. This is explained by taking into account the pressure-induced increase of the strain in our structure. The strain was calculated taking in to account that in-plane strain is not equal (due to fact that we used a-plane sapphire as a substrate) and the potential distribution in the structure was calculated self-consistently. The pressure induced increase of the built-in electric field is the same for all thicknesses of quantum wells, but becomes more pronounced for thicker quantum wells due to the quantum confined Stark effect lowering the pressure coefficients.