Polarisation has been identified as a useful tool to study cosmic magnetism. Here, we show how we compute polarisation reliably for large-scale structures threaded by magnetic fields. We present a covariant formulation of polarised radiative transfer, from which the cosmological polarised radiative transfer equation is derived. The formulation takes full account of Faraday conversion and rotation between the polarisation components and considers an explicit treatment of emission and absorption as the polarised light propagates. Relativistic and cosmological effects are implemented self-consistently within the radiative transfer formulation. We show a solution scheme for the radiative transfer calculations, which is based on the ray-tracing method, and also a set of practical demonstrations in astrophysical/cosmological settings (using a model universe obtained by the GCHMD+ simulation) to illustrate how the formulation is used the compute the all sky polarisation.