We study the mutual evolution of the orbital properties of high-mass ratio, circular, co-planar binaries and their surrounding discs, using 3D Smoothed Particle Hydrodynamics simulations. We investigate the evolution of binary and disc eccentricity, cavity structure, and the formation of orbiting azimuthal overdense features in the disc. Even with circular initial conditions, all discs with mass ratios q > 0.05 develop eccentricity. We find that disc eccentricity grows abruptly after a relatively long time-scale (∼400-700 binary orbits), and is associated with a very small increase in the binary eccentricity. When disc eccentricity grows, the cavity semimajor axis reaches values $a_{\rm cav}\approx 3.5\, a_{\rm bin}$ . We also find that the disc eccentricity correlates linearly with the cavity size. Viscosity and orbit crossing appear to be responsible for halting the disc eccentricity growth - eccentricity at the cavity edge in the range e_cav ∼ 0.05-0.35. Our analysis shows that the current theoretical framework cannot fully explain the origin of these evolutionary features when the binary is almost circular (e_bin ≲ 0.01); we speculate about alternative explanations. As previously observed, we find that the disc develops an azimuthal overdense feature in Keplerian motion at the edge of the cavity. A low-contrast overdensity still co-moves with the flow after 2000 binary orbits; such an overdensity can in principle cause significant dust trapping, with important consequences for protoplanetary disc observations.