The structure and evolution of gas flows within the cavity of a circumbinary disc surrounding the stellar components in eccentric binaries are examined via two dimensional hydrodynamical simulations. The degree to which gas fills the cavity between the circumstellar discs and the circumbinary disc is found to be greater for highly eccentric systems, in comparison to low eccentricity systems, reflecting the spatial extent over which mass enters into the cavity throughout the orbit. The pattern of the gas flow in the cavity differs for eccentric binaries from that of binaries in a circular orbit. In particular, the former reveals tightly wound gas streams and double ring-like structures for systems characterized by eccentricities, \(e \geq 0.4\), whereas the latter only reveal relatively loosely bent streams from the circumbinary disc to the circumstellar discs. Hence, the existence of the ring-like features can be a probe of sufficient non circularity of the binary orbital motion. Given that the inner edge of the circumbinary disc is not very well defined for highly eccentric systems due to the complex gas structures, it is suggested that the area of the cavity for high sensitivity imaging observations may prove to be a more useful diagnostic for probing the effectiveness of circumbinary disc clearing in the future.