Recent claims of an experimental demonstration of spontaneous spin polarisation in dilute electron gases cite{young99} revived long standing theoretical discussions cite{ceper99,bloch}. In two dimensions, the stabilisation of a ferromagnetic fluid might be hindered by the occurrence of the metal-insulator transition at low densities cite{abra79}. To circumvent localisation in the two-dimensional electron gas (2DEG) we investigated the low populated second electron subband, where the disorder potential is mainly screened by the high density of the first subband. This letter reports on the breakdown of the spin symmetry in a 2DEG, revealed by the abrupt enhancement of the exchange and correlation terms of the Coulomb interaction, as determined from the energies of the collective charge and spin excitations. Inelastic light scattering experiments and calculations within the time-dependent local spin-density approximation give strong evidence for the existence of a ferromagnetic ground state in the diluted regime.