Context. HR 4796 A is surrounded by a debris disc, observed in scattered light as an inclined ring with a high surface brightness. Past observations have raised several questions. First, a strong brightness asymmetry detected in polarised reflected light has recently challenged our understanding of scattering by the dust particles in this system. Secondly, the morphology of the ring strongly suggests the presence of planets, although no planets have been detected to date. Aims: We aim here at measuring with high accuracy the morphology and photometry of the ring in scattered light, in order to derive the phase function of the dust and constrain its near-infrared spectral properties. We also want to constrain the presence of planets and set improved constraints on the origin of the observed ring morphology. Methods: We obtained high-angular resolution coronagraphic images of the circumstellar environment around HR 4796 A with VLT/SPHERE during the commissioning of the instrument in May 2014 and during guaranteed-time observations in February 2015. The observations reveal for the first time the entire ring of dust, including the semi-minor axis that was previously hidden either behind the coronagraphic spot or in the speckle noise. Results: We determine empirically the scattering phase function of the dust in the H band from 13.6° to 166.6°. It shows a prominent peak of forward scattering, never detected before, for scattering angles below 30°. We analyse the reflectance spectra of the disc from the 0.95 μm to 1.6 μm, confirming the red colour of the dust, and derive detection limits on the presence of planetary mass objects. Conclusions: We confirm which side of the disc is inclined towards the Earth. The analysis of the phase function, especially below 45°, suggests that the dust population is dominated by particles much larger than the observation wavelength, of about 20 μm. Compact Mie grains of this size are incompatible with the spectral energy distribution of the disc, however the observed rise in scattering efficiency beyond 50° points towards aggregates which could reconcile both observables. We do not detect companions orbiting the star, but our high-contrast observations provide the most stringent constraints yet on the presence of planets responsible for the morphology of the dust.