Channeling of light relativistic particles in crystals is accompanied by intense radiation emission known as channeling radiation. Typically all calculations of channeling radiation aim in getting the total radiation intensity and its dependence on the parameters of particles and crystals. In the same time, since the discovery, the angular behaviours of channeling radiation have been studied just in a few works, in which only a polar dependence of the radiation intensity near the forward direction is estimated. However, simple analysis of the interaction potential predicts very specific features to be observed in the angular distributions of channeling radiation, especially at axial regime. In this work, for the first time, the expressions for angular and spectral distributions of electromagnetic radiation at axial channeling of relativistic charged particles in thin crystals are analytically refined within the QED theory. Obtained results allows predicting complex structures of radiation intensity and polarisation distributions. The results obtained might be of special interests for experimental studies.