We present both a theoretical and experimental analysis of nonlinear polarization rotation in an optical fibre. Starting from the coupled nonlinear Schrödinger equations an analytical solution for the evolution of the state of polarization, valid for fibres with large linear birefringence and quasi cw input light with arbitrary polarization, is given. It allows us to model straightforwardly go-and-return paths as in interferometers with standard or Faraday mirrors. In the experiment all the fluctuations in the linear birefringence, including temperature- and pressure-induced ones, are successfully removed in a passive way by using a double pass of the fibre under test with a Faraday mirror at the end of the fibre. This allows us to use long fibres and relatively low input powers. The match between the experimental data and our model is excellent, except at higher intensities where deviations due to modulation instability start to appear.