We investigate whether the rings, lopsided features and horseshoes observed at millimetre (mm) wavelengths in transitional discs can be explained by the dynamics of gas and dust at the edge of the cavity in circumbinary discs. We use 3D dusty smoothed particle hydrodynamics calculations to show that binaries with mass ratio ... drive eccentricity in the central cavity, naturally leading to a crescent-like feature in the gas density, which is accentuated in the mm dust grain population with intensity contrasts in mm continuum emission of 10 or higher. We perform mock observations to demonstrate that these features closely match those observed by the Atacama Large Millimetre/Submillimetre Array, suggesting that the origin of rings, dust horseshoes and other non-axisymmetric structures in transition discs can be explained by the presence of massive companions. (ProQuest: ... denotes formulae/symbols omitted.)