This disclosure relates to a rechargeable battery cell having a positive electrode, a negative electrode, an electrolyte, which comprises a conducting salt, and a separator, which is arranged between the positive electrode and the negative electrode. The negative electrode and the positive electrode are each an insertion electrode. The electrolyte is based on SO2. The separator comprises a separator layer which is an organic polymer separator layer. The thickness of the organic polymer separator layer, relative to the loading of the positive insertion electrode with active material per unit area, is less than 0.25 mm3/mg.