The polarisation of exciton-polariton emission is used to determine parameters of the interaction Hamiltonian of cavity polaritons. Linear polarisation of the polariton emission under linearly polarised excitation is theoretically analysed and shown to be determined by the ratio of the interaction strengths of polaritons with opposite and parallel spins. The experimentally observed inversion of the linear polarisation of the emission with respect to that of the exciting light indicates the dominant role of the exchange interaction in the polariton-polariton scattering. A comparison with the theory yields the sign of the term in the Hamiltonian describing the interaction of two polaritons with opposite spins, as well as its relative value with respect to the main term responsible for the scattering of polaritons with parallel spins.