We present the results of two-dimensional hydrodynamic simulations of self-gravitating circumbinary discs around binaries whose parameters match those of the circumbinary planet-hosting systems Kepler-16, Kepler-34 and Kepler-35. Previous work has shown that non-self-gravitating discs in these systems form an eccentric precessing inner cavity due to tidal truncation by the binary, and planets which form at large radii migrate until stalling at this cavity. Whilst this scenario appears to provide a natural explanation for the observed orbital locations of the circumbinary planets, previous simulations have failed to match the observed planet orbital parameters. The aim of this work is to examine the role of self-gravity in modifying circumbinary disc structure as a function of disc mass, prior to considering the evolution of embedded circumbinary planets. In agreement with previous work, we find that for disc masses between one and five times the minimum mass solar nebula (MMSN), disc self-gravity affects modest changes in the structure and evolution of circumbinary discs. Increasing the disc mass to 10 or 20 MMSN leads to two dramatic changes in disc structure. First, the scale of the inner cavity shrinks substantially, bringing its outer edge closer to the binary. Secondly, in addition to the eccentric inner cavity, additional precessing eccentric ring-like features develop in the outer regions of the discs. If planet formation starts early in the disc lifetime, these changes will have a significant impact on the formation and evolution of planets and precursor material.