The change in the ellipticity of a laser beam that passes through plasma, due to the Cotton-Mouton effect can provide additional information on the plasma density. This approach, complementary to the more traditional interferometric methods, has been implemented recently using the JET interferometer-polarimeter with a new set-up. Routine Cotton-Mouton angle measurements are made on the vertical central chords simultaneously with the Faraday Rotation angle data. This new data is used to provide robust line-integrated density measurements in difficult plasma scenarios, with strong ELMs or pellets. These always affect interferometry, causing fringe jumps and preventing good control of the plasma density. A comparison of line-integrated density from polarimetry and interferometry measurements shows an agreement within 10%. Moreover, in JET the measurements can be performed close to a reactor relevant range of parameters, in particular at high densities and temperatures. This provides a unique opportunity to assess the quality of the Faraday rotation and Cotton-Mouton angle measurements where both effects are strong and mutual non-linear interaction between the two effects takes place.