We report on the observation of symmetry breaking and the circular photogalvanic effect in CdxHg1-xTe alloys. We demonstrate that irradiation of bulk epitaxial films with circularly polarized terahertz radiation leads to the circular photogalvanic effect (CPGE) yielding a photocurrent whose direction reverses upon switching the photon helicity. This effect is forbidden in bulk zinc-blende crystals by symmetry arguments; therefore, its observation indicates either the symmetry reduction of bulk material or that the photocurrent is excited in the topological surface states formed in a material with low cadmium concentration. We show that the bulk states play a crucial role because the CPGE was also clearly detected in samples with noninverted band structure. We suggest that strain is a reason for the symmetry reduction. We develop a theory of the CPGE showing that the photocurrent results from the quantum interference of different pathways contributing to the free-carrier absorption (Drude-like) of monochromatic radiation.