Flexoelectric coupling gives rise to a linear electro-optic response in cholesterics (flexoelectrooptic effect) with a uniformly lying helix (ULH) structure and this electro-optic effect is strongly reliant on the homogeneity and quality of the texture. The ULH structure, unfortunately, is complicated in itself and may be perturbed by factors such as dielectric coupling, surface/liquid crystal interactions and phase transitions, and often there is a tendency for relaxation into the Grandjean texture (standing helix structure) with time. Hence, in order to exploit the flexoelectro-optic effect in cholesterics any instability of the ULH structure must be ruled out. We have overcome these problems by incorporating a polymer network by means of photopolymerization of a reactive monomer added to the cholesteric. The volume stabilized ULH structure still exhibits the flexoelectro-optic effect, it is stable and it is also retained after heating to the isotropic phase and going back to the cholesteric phase. In addition to the flexoelectro-optic mode, the ULH structure is of interest in an electro-optic mode characterized by a pure phase-shift with no change in amplitude (transmittance). This mode, which has obvious applications in spatial light modulators, optical computing devices and electrically controlled kinoforms and phase holograms working without polarizers, is also briefly discussed.