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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 over-dense 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 ($\sim 400\textrm{--}700$ binary orbits), and is associated with a very small increase in the binary eccentricity. When disc eccentricity grows, the cavity semi-major 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 $e_{\rm cav}\sim 0.05\textrm{--} 0.35$. Our analysis shows that the current theoretical framework cannot fully explain the origin of these evolutionary features when the binary is almost circular ($e_{\rm bin}\lesssim 0.01$); we speculate about alternative explanations. As previously observed, we find that the disc develops an azimuthal over-dense feature in Keplerian motion at the edge of the cavity. A low contrast over-density still co-moves with the flow after 2000 binary orbits; such an over-density can in principle cause significant dust trapping, with important consequences for protoplanetary disc observations.